4 b + 3 o2 → 2 b2o3 if 8 moles of b and 4 moles of o2 are allowed to react, how many moles of b2o3 can be formed?

Answers

Answer 1

The number of moles of  b2o3 that will be formed is determined as 4 moles.

Limiting reagent

The limiting reagent is the reactant that will be completely used up.

4 b + 3O₂ → 2b₂O₃

from the equation above;

4 b ------------> 2 b₂O₃

2b ------------> b₂O₃

2 : 1

3O₂  -------------> 2b₂O₃

3  :  2

b is the limiting reagent, thus, the amount of b2o3 to be formed is calculated as;

4 b ------------> 2 moles of  b2o3

8 moles -------> ?

= (8 x 2)/4

= 4 moles

Thus, the number of moles of  b2o3 that will be formed is determined as 4 moles.

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Related Questions

A certain hydrocarbon has a chemical composition of 79.85% of carbon and 20.15% of hydrogen. The molar mass is 60.16 g/mol. What is the molecular formula for this compound

Answers

The molecular formula for the compound is [tex]C_{4} H_{8}[/tex] .

Given:

% of C = 79.85%

% of H = 20.15%

Let the mass of the compound be 100g, then

Mass of C = 70.85 g

Mass of H = 20.15 g

Molar mass = 60.15 g/mol

Moles of Carbon = [tex]\frac{79.85}{12.01 g/mol}[/tex]

                             = [tex]6.64 mol[/tex]

Moles of Hydrogen = [tex]\frac{20.15}{1.00794 g/mol}[/tex]

                                 = [tex]19.99 mol[/tex]

And we divide both sides by the lower quantity;

[tex]C_{\frac{6.64 mol}{6.64 mol} } H_{\frac{19.99 mol}{6.64 mol} }[/tex] ≅ CH₂

And [tex](empirical formula)_{n} = molecular formula[/tex]

60.15 g/mol = n × ( 12.01 + 2 × 1.00794)

n = 4

Therefore, the molecular formula for the compound is [tex]C_{4} H_{8}[/tex] .

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What is one disadvantage of using fossil fuels?

Answers

Answer:

Fossil fuels contribute to greenhouse gases, which is one of their major disadvantages. The most harmful for the environment is coal because it has many more harmful combustion products than other fossil fuels.

green house affects environment affected by killings

Which of the following is not a type of structural isomerism? A. Functional group B. Optical C. Chain D. Positional

Answers

Answer:

B. Optical

Explanation:

First, let's go through what isomerism is. Isomerism is the relation of two or more compounds, radicals, or ions that are composed of the same kinds and numbers of atoms but differ from each other in structural arrangement (structural isomerism), as CH3OCH3 and CH3CH2OH, or in the arrangement of their atoms in space and therefore in one or more properties.  There are 5 types of structural isomerism. They are chain isomerism, position isomerism, functional group isomerism, metamerism, and tautomerism. This would mean that these types of structural isomerism that are in the options would be eliminated as the question ask which of the "following" is not a type of structural isomerism. This would leave the only option available which is Option B. Optical Isomerism. So instead of being a structural isomerism, it is a type of stereoisomerism. Stereoisomerism is the arrangement of atoms in molecules whose connectivity remains the same but their arrangement in space is different in each isomer.

Therefore, the answer is Option B. Optical.

Select all correct statements from below. a. Recrystallization is a technique used to purify solid compounds based on solubility differences at different temperatures. b. Toluene is a clear, colorless liquid which becomes a vapor when exposed to air at room temperature. Do not breathe in. Always handle it in the fume hood. c. Filtration is a technique to separate solid from liquid(s). d. There are two different filtration techniques: Gravity Filtration and Vacuum Filtration.

Answers

All are correct statements:-

Recrystallization is a technique for purifying solid compounds. Solids tend to dissolve more in hot liquids than in cold liquids. During recrystallization, the impure solid compound is dissolved in a hot liquid until the solution is saturated, after which the liquid is cooled.

Toluene is a clear, colorless liquid that evaporates in the air at room temperature. Toluene smoke has a pungent or sweet odor, which is a sign of exposure. Toluene is typically used as a mixture with other solvents and chemicals such as paint pigments. Inhalation of small doses of toluene vapor can cause mild headaches, dizziness, drowsiness, or nausea.

Filtration is the process of separating an insoluble solid from a liquid. When filtering a mixture of sand and water: the sand remains on the filter paper (it becomes a residue). Water flows through the filter paper (it becomes a filtrate). Gravity filtration and vacuum or suction filtration are the types of filtration.

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What is the ratio by mass of these compounds a. 2na+cl2 =2nacl? b.h2o +nao=2naoh? c.hcl+naoh=nacl+h2o?

Answers

The ratio of the mass of compounds:

a. 2Na + Cl[tex]_{2}[/tex] → 2NaCl = 46 + 70 → 46 : 70

b. H[tex]_{2}[/tex]O + NaO → 2NaOH = 1 : 8 + 23 : 16 → 23 : 16 : 1

c. HCl + NaOH → NaCl + H[tex]_{2}[/tex]O = 1 : 35 + 23 : 35 → 23 : 35 + 1: 8

What is a  molecular mass?

Molecular mass refers to the total sum of the masses of the atoms or components that make up the molecule.

Calculation:

a. 2Na + Cl[tex]_{2}[/tex] → 2NaCl

The atomic mass of Na= 23The atomic mass of Cl= 35

(Na x 2) + (Cl x 2) → (Na x 2) : (Cl x 2)

(23 x 2) + (35 x 2) → (23 x 2) : (35 x 2)

46 + 70 → 46 : 70

b. H[tex]_{2}[/tex]O + NaO → 2NaOH

The atomic mass of H = 1The atomic mass of O= 16Atomic mass of Na= 23

(H x 2) : (O x 1) + (Na x 1) : (O x 1) → (Na x 2) : (O x 2) : (H x 2)

(1 x 2) : (16 x 1) + (23 x 1) : (16 x 1) → (23 x 2) : (16 x 2) : (1 x 2)

2 : 16 + 23 : 16 → 46 : 32 : 2

1 : 8 + 23 : 16 → 23 : 16 : 1

c. HCl + NaOH → NaCl + H[tex]_{2}[/tex]O

The atomic mass of H= 1The atomic mass of Cl= 35The atomic mass of Na= 23The atomic mass of O= 16

(H x 1) : (Cl x 1) + (Na x 1) : (Cl x 1) → (Na x 1) : (Cl x 1): (H x 2) : (O x 1)

(1 x 1) : (35 x 1) + (23 x 1) : (35 x 1) → (23 x 1) : (35 x 1) : (1 x 2) : (16 x 1)

1 : 35 + 23 : 35 → 23: 35 + 2: 16

1 : 35 + 23 : 35 → 23 : 35 + 1: 8

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If the molar mass of x (hco3) is 162 g/mol, determine the relative atomic mass of x.

Answers

The relative atomic mass of x is 101 u.

Molar mass is calculated by adding the atomic mass of all the elements in a compound.

Molar mass of x(HCO₃) =162 g/mol

Atomic mass of H = 1 g/mol

Atomic mass of C =12 g/mol

Atomic mass of O = 16 g/mol

Therefore, molar mass of x(HCO₃) will be

= x + 1 + 12 + 3 x 16

We know that:

x + 1 + 12 + 3 x 16=162

x + 61 = 162

x = 101 g/mol

The relative atomic mass of x will be 101 u.

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HELP!!!! Will mark give 5 stars and thank!! Please!
Many types of chemical reactions include a thermochemical component
In a paragraph, compare and contrast endothermic and exothermic
reactions, including a real-world example of each type.

Answers

Answer:

An endothermic reaction is a reaction where heat is taken in from the surroundings. This could be in the process of vaporisation from liquid to gas. However an exothermic reaction is when heat is given out to the surroundings. An example of this would be condensation gas to liquid!

Explanation:

Which sentences describe the logistic growth model?
There are three different phases of the S-shaped curve. At first, growth is exponential because individuals are few and resources are plenty. This growth model occurs in a situation where resources are plenty and individuals are few to consume the resources. Population growth decreases as resources become limited. When a population size reaches the carrying capacity of its environment, the population growth slows down or stops completely. The model looks like a J-curve.

Answers

The sentences describe the logistic growth model is when a population size reaches the carrying capacity of its environment, the population growth slows down or stops completely.

What is logistical growth?

Logistic or sigmoidal growth involves exponential population growth followed by a steady reduction in population growth until the population size stabilizes, assuming an S-shaped curve.

In this case, we can say this affirmation is true for the S-curve, but not the J-curve.

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1.Tritium, of hydrogen-3, is prepared by bombarding lithium-6 with neutrons. A 0.250-mg sample of tritium decays at the rate of 8.94 x 1010 disintegrations per second. What is the decay constant (in per sec) of tritium, whose atomic mass is 3.02 amu

Answers

The decay constant (in per sec) is  1.79* 10^ -9/sec

The rate of decay is 8.94 x 1010 nuclei/s. The number of nuclei in the sample is

The rate equation is rate = kNt. Solve for k.

An exponential function has a variable exponent, a positive base, and a base that is not equal to one.

For instance, F (x) = 4x is an exponential function since the exponent is set rather than variable.

Instead of being an exponential function, f (x) = x3 is a fundamental polynomial function.

The graphs of exponential functions are continuously curved and never reach a horizontal asymptote.

Several real-world phenomena are governed by exponential or logarithmic functions.

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the authors imply that the response of various officials to attempts to measure their countries' carbon stock through field surveys has been

Answers

The measurement of the countries' carbon stock through field surveys by has been unhelpful, because the officials don't make their countries' land holdings readily available for study.​

What is an inference?

An inference can be defined as an act through which a reader can deduce the meaning and message (information) that is associated with certain text in a passage, especially through induction.

In this scenario, we can infer and logically deduce that the author implied that the measurement of the countries' carbon stock through field surveys by has been unhelpful, because the officials don't make their countries' land holdings readily available for study.​

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Complete Question:

The authors imply that the response of various officials to attempts to

measure their countries' carbon stock through field surveys has been:

A. unhelpful, because they fear that jobs for their countries' scientists will be lost.

B. helpful, because their countries have invested significantly in technology to allow studies to expand.

C. helpful, because their countries stand to benefit from universal carbon data that the studies will uncover.

D. unhelpful, because they do not make their countries' land holdings readily available for study.​

A 25 kg rock is placed in a graduated cylinder with water.the volume of the fluid is 18.3ml.calculate the density of the rock in g/ml

Answers

Answer:

=> 1366.120 g/mL.

Explanation:

To determine the formula to use in solving such a problem, you have to consider what you have been given.

We have;

mass (m)     = 25 Kg

Volume (v) = 18.3 mL.

From our question, we are to determine the density (rho) of the rock.

The formula:

[tex]p = \frac{m}{v}[/tex]

First let's convert 25 Kg to g;

1 Kg    = 1000 g

25 Kg = ?

[tex]= \frac{25 × 1000}{1}[/tex]

= 25000 g

Substitute the values into the formula:

[tex]p = \frac{25000 g}{18.3 ml}[/tex]

= 1366.120 g/mL.

Therefore, the density (rho) of the rock is  1366.120 g/mL.

In a titration of 25.0 ML of 0.40m NaOH is used to neutralize 10.0 ML of HCL. Calculate the molarity of the acid.

Answers

Answer:

=> 1.0 M

Explanation:

The question is asking us to find the molarity of the acid (HCl).

We have been provided with;

25.0 mL of 0.40 M NaOH10.0 mL of HCl

We know that molarity (M) of a solution is contained in 1 L or 1000 mL or 1000 cm³.

This means that;

0.40 M is contained in 1000 mL.

X mol is contained in 25.0 mL

[tex] = \frac{25 \: \times \: 0.40}{1000} \\ = 0.01 \: moles[/tex]

These 0.01 moles is contained in 10 mL of HCl.

To find the molarity of the acid;

0.01 moles is contained in 10 mL

x mol is contained in 1000 mL

[tex]x \: mol \: = \frac{0.01 \times 1000}{10} \\ = 1.0 \: mol[/tex]

= 1.0 M

Therefore the molarity of the acid (HCl) is 1.0 M

Which chemical formula corresponds to this structural formula? h6c6h6h2 c14h6 c6h6 c2h6o

Answers

C₂H₆O is referred to the chemical formula corresponds to this structural formula and is denoted as option D.

What is Chemical formula?

This contains information about the chemical proportion of atoms present in a molecule.

In this scenario, there are two carbon atoms, six hydrogen atoms and one oxygen atom which can be written as C₂H₆O. This is therefore the most appropriate choice in this scenario.

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Answer: D.) C6H14

Explanation: i hope this helps (this is for another question you might have tho) :)

1. A sample of a gas is occupying a 500 mL container at a pressure of 1.4 atm and a temperature of 25 °C.
If the temperature is increased to 50 °C and the pressure is increased to 2.7 atm, what is the new
volume?

Answers

The new volume of a sample of gas initially occupying a 500 mL container at a pressure of 1.4 atm and a temperature of 25 °C is 281.01mL.

How to calculate volume?

The volume of a gas can be calculated using the following formula:

P1V1//T1 = P2V2/T2

Where;

P1 = initial pressureP2 = final pressureV1 = initial volumeV2 = final volumeT1 = initial temperatureT2 = final temperature

1.4 × 500/298 = 2.7 × V2/323

2.348 × 323 = 2.7V2

758.72 = 2.7V2

V2 = 281.009mL

Therefore, the new volume of a sample of gas initially occupying a 500 mL container at a pressure of 1.4 atm and a temperature of 25 °C is 281.01mL.

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If an electron in an atom gains energy to go from a lower energy level to a higher energy level, it ______________

Answers

If an electron in an atom gains energy to go from a lower energy level to a higher energy level, it is called Excited energy state.

Ground state energy: The lowest energy state for an electron is called its ground state, which is the energy level it typically resides in. Each electron has a limit on how much energy it can have while still remaining a part of its atom. It is the most stable state of electron.

Excited state energy: An electron is in an excited state when it momentarily possesses an energy state higher than its ground state. If an electron receives additional energy, such as when it absorbs a photon, or packet, of light, or collides with an adjacent atom or particle, it can become excited. As these excited state energy level are unstable. So while coming back to ground state electrons emit radiations suitable wavelength.

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Pls answer asap i will mark u brainlistl

Answers

Answer:

X = 350 kJ/mol

Explanation:

According to the question:

Energy needed when breaking bonds  +  1640 kJ/mol   =   Energy released when forming bonds

2 (C - C) + 8 (C - H) + 5 (O = O) + 1640 = 6(C = O) + 8(O - H)

⇒ 2 (X) + 8 (410) + 5 (500) + 1640 = 6 (740) + 8 (460)

⇒ 2X  +  7420  =  8120

⇒ 2X = 700

X = 350 kJ/mol

how would the equilibrium change if the temperature were increased in SO2(g)+NO2(g) --> SO3(g) +heat?

Answers

Answer:

D. The amount of nitrogen dioxide and sulfur dioxide would increase.

Explanation:

Because the reaction is exothermic, heat is a product. According to Le Chaetelier's Principle, a system in equilibrium will adjust itself so as to relieve any stress placed upon it. If the temperature of the system increases, there are more products, and therefore the system is no longer at equilibrium. Thus, it will shift to favor the reactant side of the equation, where sulfur dioxide and nitrogen dioxide are located. This makes the answer D.

Edit: Brainly thinks that the correct spelling of 'Le Chaetelier' is a bad word so that's why it is spelled wrong lol.

What is 1 atmospheric pressure? ​

Answers

Answer:

101325 pascal

Explanation:

i dont cap

Answer:

See below

Explanation:

1 atmosphere = 101 325 Pascals = 760 mm Hg = 14.6959 psi

Decide whether each proposed multiplication or division of measurement is possible. If it is possible, write the result in the last column of the table.

Answers

Answer:

See attached image.

Explanation:

The explanations are on the attachment.  The numerical results are below.

1.  63g/7cm^3 = 9 g/cm^3

2.  The m or mm must be converted so that the units are the same.  1 m = 1000 mm.  I'll convert the meters to mm:  0.080 m = 80 mm.

480 mm^2/80 mm = 6 mm

3.  L times L makes no physical sense, unless this is a new Star Wars technique for making dark matter.  Entertaining, but useless.

what could you do to increase the electrical force between two charged particles by a factor of 16

Answers

Increasing one charged particle by 16 will lead to increasing the electrical force between two charged particles by a factor of 16.

What is Electrical force?

This is referred the attractive or repulsive interaction between any two charged bodies present.

F= kq1q2/r²

F1/F2= kq1q2/r² / 16kq1q2/r²

F1/F2 = 1/16

F2 = 16F1

This is therefore how to increase the electrical force between two charged particles by a factor of 16.

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can someone help me with this?

Answers

Answer:

I see "photosynthesis" and "cellular respiration". I wonder if photosynthesis has something to do with the sun.

Explanation:

You need 440 mL of a 30% alcohol solution. On hand, you have a 40% alcohol mixture. How much of the 40% alcohol mixture and pure water will you need to obtain the desired solution

Answers

110ml of the 40% alcohol mixture and pure water will  need to obtain the desired solution

Given that 0.30 * 440 = 132 mL of pure alcohol needed

132 mL = 0.40 * x mL of 0.4

x = 330 mL of 70%

440 - 330 = 110 mL of H2O

Water content differs

If you have 440 mL of a 30% alcohol mixture, then (440mL)*(0.30) = 132mL of that solution is alcohol.

Similarly, if you have x mL of a 40% alcohol mixture, then (x mL)(0.40) = 0.40x mL of that solution is alcohol.

When you combine these two liquids, you will have (440 + x) mL of liquid and you want it to be 40% alcohol.

Hence  110ml of the 40% alcohol mixture and pure water will  need to obtain the desired solution

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An electron can be added to halogen atom to force a halide ion with

Answers

An electron can be added to halogen atom to force a halide ion with 8 valence electrons

What is an atom?

An atom can be defined as the smallest part of an element which can take part in a chemical reaction.

However whenever, an electron is added to halogen atom to force a halide ion with 8 different valence electrons

So therefore; an electron can be added to halogen atom to force a halide ion with 8 valence electrons

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Still using the reaction from the video, what is the limiting reagent when 2 moles of Al are reacted
with 2 moles of O₂? About how many total reactions can you run?
O Al, 0.67 reactions
O Al, 0.5 reactions
Oxygen, 0.67 reactions
O Oxygen, 0.5 reactions

Answers

The limiting reagent will be Al

What are limiting reagents?

They are reagents that limit the quantity of products that are formed in reactions.

From the equation of the reaction:

[tex]4Al + 3O_2 --- > 2Al_2O_3[/tex]

The mole ratio of Al to O2 is 4:3.

With 2 moles of Al and 2 moles of O2, Al becomes limiting while O2 is in excess.

With 2 moles of O2, the amount of Al required should be:

                          2 x 4/3 = 2.67 moles.

With 2 moles of Al, the amount of O2 required should be:

                    2 x 3/4 = 1.5 moles

Thus, O2 is in excess by 0.5 moles.

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Please help me by giving me an drawing , it’s urgent !! Or writing explanation but drawing is easier.

Answers

Answer:

13 Protons, 14 Neutrons, and 13 electrons.

Explanation:

See Picture Below

I have labeled all the numbers and the diagram.

I hope it helped

Increasing technology addiction among the youth write a letter to editor

Answers

Answer:

these two would help you

Explanation:

have a good day ᕕ( ᐛ )ᕗ

What is the IUPAC name for this compound?

Answers

Answer:

valeric acid

Explanation:

I don't know exactly. But try this one.

Answer:

IUPAC NAME: PENTANOIC ACID

COMMON NAME: VALERIC ACID

PLEASE HELP, CANT SEEM TO FIGURE THIS OUT!

Answers

Answer:

independent: amount of baking powder

dependent: the banana bread that it produces

constants: the amount of other ingredients/the other ingredients, the type of baking powder, rest of the baking process (heat, temperature, timing of steps), and who's tasting the bread.

Explanation:

The independent variable is the thing that we are directly changing.

We usually change this to test out differences between different amounts of this variable;

This variable is the "x" variable in a function or graph, if it helps you to think of it as that.

The dependent variable is the thing that changes because of the independent variable

Once again, if you think of a graph or function, this would be the "y" variable--it changes in relation to x

The constants are the things that stay the same no matter what the changing variables are

This element is key to an experiment--an experiment would be almost pointless without it. We need to see what is actually changing as a result of the independent and intentional changes.

Here's an example:

Let's say I want to test out how much condensation forms on a bottle based on the temperature of the liquid inside.

I will be changing the temperature of the liquid inside, meaning that this is the independent variable

I will be expecting/looking for a change in the condensation because of my change in the independent variable, meaning that this is the dependent variable

In my experiment, there are some things I need to make sure don't change, so that I can see the effect of my change in the temperature directly--perhaps I need to keep the same bottle shape and size, the same amount of liquid, the same location, the same type of liquid, the same amount of time I let it sit for, etc.  meaning that these are my constants.

So, with all of this in mind, let's take a look at our experiment given.

Here, I will be changing the amount of baking powder that I use, whilst observing the change in the banana bread that it directly produces.

There are a few things I must keep constant: the amount of the other ingredients, the rest of the baking process (heat/temperature, mixing time, etc.), and the type of baking powder I use

There is another consideration that I probably want to keep consistent: who is deciding the taste of the bread. If the person switches, then I might get a different opinion for the same recipe.

hope this helps! have a lovely day :)

Option 2 involves conducting an experiment to find the ideal amount of baking powder to add to a batch of banana bread.

The amount of baking powder served as the independent variable. The goal of this experiment is to determine the ideal amount of baking powder to use in each batch of banana bread.

Dependent Variable: The standard of banana bread served as the dependent variable. It is called the outcome you are measuring or observing in response to a change in the independent variable. In this instance it could be the taste, texture or texture of banana bread.

Constant: Some variables must remain constant throughout the experiment to ensure that only the independent variable has an effect on the dependent variable. Following are some possible constants in this experiment:

Banana Bread recipe except with variable amounts of baking powder.Baking time and temperature.Ingredients (such as bananas, flour, sugar, etc.) that are not baking powder.An oven for baking.

By holding these variables constant, you can isolate the effect of different amounts of baking powder on the quality of the banana bread and determine the exact amount needed for best results.

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When uranium ionizes and becomes u 238 5 , there are _____ protons, _____ neutrons, and _____ electrons.

Answers

The ionized uranium (238 [tex]U^{5+}[/tex]) has 92 protons, 146 neutrons and 87 electrons.

What is Uranium(238) called?

The U²³⁸ is a stable isotope of Uranium. It cannot sustain a chain reaction.

The atomic number for uranium is 92 and its atomic mass is 238.

How many protons, electrons and neutrons are there?

The atomic number for U²³⁸ is 92.

So, the number of protons or electrons = 92

Then, the number of neutrons = atomic mass - number of protons

⇒ 238 - 92 = 146

How many protons, electrons and neutrons are there in the ionized Uranium?

The Uranium is ionized and becomes ²³⁸U⁵⁺.

So,

The number of protons = 92

The number of electrons = 92 - 5 = 87 (Since uranium is ionized by 5+ electrons i.e., removing 5 electrons)

The number of neutrons = atomic mass - number of protons

= 238 - 92 = 146

Thus, when uranium ionizes and becomes ²³⁸U⁵⁺, there are 92 protons, 146 neutrons, and 87 electrons.

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4NH3(g) + 5O2(g) 4NO(g) + 6H2O(g)

In a reaction that produced 34.8 L of water vapor, what volumes of ammonia and oxygen were consumed?

Answers

1. The volume of ammonia consumed in the reaction is 23.2 L

2. The volume of oxygen consumed in the reaction is 29 L

Balanced equation

4NH₃(g) + 5O₂(g) --> 4NO(g) + 6H₂O(g)

From the balanced equation above,

6 L of H₂O were produced from 4 L of NH₃ and 5 L of O₂

1. How to determine the volume of ammonia, NH₃ consumed

From the balanced equation above,

6 L of H₂O were produced from 4 L of NH₃

Therefore,

34.8 L of H₂O will be produced from = (34.8 × 4) / 6 = 23.2 L of NH₃

Thus, 23.2 L of NH₃ were consumed

2. How to determine the volume of oxygen, O₂ consumed

From the balanced equation above,

6 L of H₂O were produced from 5 L of O₂

Therefore,

34.8 L of H₂O will be produced from = (34.8 × 5) / 6 = 29 L of O₂

Thus, 29 L of O₂ were consumed

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Other Questions
A ____ is a character who is used to bring out the feelings and personality of the main character Please Help Me Ill Appreciate Your Help Please And Thank You! Fun Time Corp. has decided to move production of its board games for children and adults from the United States to Mexico to realize cost savings. At the same time, the company has decided to make Spanish-language versions of the games and distribute them in Central and South America. Most likely Fun Time is pursuing a strategy of ________. Multiple Choice Two points have the coordinates P (6, -3,9) and Q (3, -6, -3). A point R divides line PQ internally in the ratio 1:2. The position vectors of P, Q and Rare p, q and r respectively.(a) Express the position vector of p and q.i. In terms of p and q.ii. In terms of i, j and k(b) Hence state the coordinates of R. A driver in a 2,000 kg SUV moving at 15 m/s crashes into a stopped car, causing it to be propelled forward and the truck to be slowed to 10 m/s. What is the work done on the SUV by the stopped car The case of Wickard v. Filburn concerned federal legislation designed to alleviate agricultural woes attributed to what what is the significance of test cross Consider the following situations: (a) A survey of 18,87518,875 people aged 1818 to 2525 reported that 55.1U.1% drank alcohol in the past month. (b) In a study of work stress, 250250 restaurant workers were asked about the impact of work stress on their personal lives. (c) In a study of Monarch butterflies, 5555 milkweed plants in a Yosemite Valley were randomly sampled. The average number of Monarch eggs per plant was 0.73.was 0.73. Identify the population and sample for each of the situations.1. 18.875 people age 18 to 25 2. All people aged 18 to 25 3. Proportion of 55.1% 4. All restaurant workers 5. 250 restaurant workers 6. 55 milkweed plants 7. All milkweed plants in Yosemite Valley 8. Average of 0.73a. Population b. Sample The list below gives the location of friends who are scuba diving together.Mallory is exploring at an elevation of -25 feet.Jacob is standing on the boat, at an elevation of 15 feet.Eva just jumped in and is 5 feet below the surface of the water.Which inequality correctly compares the distance of the scuba divers from the surface of the water?Eva > MalloryMallory < JacobJacob < EvaMallory > Eva Expand. (n^2 -3n +1)(2n + 3) = Create a python program that converts number grades to letter grades.Console Letter Grade Converter Enter numerical grade: 90 Letter grade: A Continue? (y/n): y Enter numerical grade: 88 Letter grade: A Continue? (y/n): y Enter numerical grade: 80 Letter grade: B Continue? (y/n): y Enter numerical grade: 67 Letter grade: C Continue? (y/n): y Enter numerical grade: 59 Letter grade: F Continue? (y/n): n Bye! Specifications The grading criteria is as follows: A 88-100 B 80-87 C 67-79 D 60-66 F John gets a weekly allowance of $20 from his parents. The only thing he has a real interest in buying is a big slice of pizza after school for $2 per slice. Below shows his marginal utility for each life consumed (see image). a) What is the optimal quantity of pizza slices for John to buy? Explain. (For now, completely ignore the funnel cake column). b) If John purchased 8 slices, what total utility would he enjoy?c) The school starts selling funnel cakes for $4, which John discovers offers the marginal utility per cake shown on the same table. Complete a table that shows the marginal utility per dollar for each slice of pizza and each funnel cake (separate columns). d) Assuming Johns parents do not allow him to use any savings, what is his optimal consumption bundle of pizza and funnel cakes? Explain. e) At Johns optimal consumption bundle, what total utility will he gain? According to the synthetic division below, which of the following statementsare true?Check all that apply.54 -17 -1520 153 04A. (4x2-17x-15) - (x + 5) = (4x + 3)B. The number 5 is a root of F(x) = 4x - 17x - 15.OC. (4x2-17x-15) - (x - 5) = (4x + 3)D. (x+5) is a factor of 4x2-17x-15.E. The number -5 is a root of F(x) = 4x-17x-15.OF. (x-5) is a factor of 4x2 - 17x-15. Which aspects of the physical assessment should the nurse include for a complete understanding of the client's physical health? To make a small vase, elisa uses no more than 4.5 ounces of clay. to make a large vase, she uses at least 12 ounces of clay. which compound inequality represents the number of ounces of clay, c, that elisa uses to make one vase of either size? An 80-kg hiker climbs to the top of a tall hill and builds up 470,000 j of gravitational potential energy. how high did the hiker climb? round the answer to the nearest hundred. meters The efficiency gains resulting from a just-in-time inventory management system will allow a firm to reduce its level of inventories permanently by $444,000. What is the most the firm should be willing to pay for installing the system Solve for x.3(x + 5)-2(x+2)=201913 The average temperature in an estuary is __________.39C35C40C45C A(n) _____ system is a branch of decision support systems (DSSs) that gives managers easy access to internal and external data and typically includes drill-down features and a digital dashboard for examining and analyzing information.