May be solved by the molar volume method (Section 14.7 ) or...

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back- ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied. The reaction chamber in a modified Haber process for making ammonia by the direct combination of its elements is operated at $575^{\circ} \mathrm{C}$ and 248 atm. How many liters of nitrogen, measured at these conditions, will react to produce $9.16 \times 10^{3}$ grams of ammonia?

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
The reaction chamber in a modified Haber process for making ammonia by the direct combination of its elements is operated at $575^{\circ} \mathrm{C}$ and 248 atm. How many liters of nitrogen, measured at these conditions, will react to produce $9.16 \times 10^{3}$ grams of ammonia?

Key Concepts

Molar Volume

Molar volume is the volume occupied by one mole of a gas at a given set of conditions, often used at standard temperature and pressure or other defined conditions. This concept simplifies the calculation of gas volumes by providing a direct relationship between the number of moles of a gas and its volume under specific conditions, making it a useful tool for solving stoichiometric problems involving gases.

Ideal Gas Law

The ideal gas law, represented by the equation PV = nRT, relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. This law provides a model for predicting the behavior of gases under various conditions, and it is fundamental for converting between different state variables when dealing with gaseous systems.

Stoichiometry

Stoichiometry involves the quantitative relationship between the reactants and products in a balanced chemical reaction. It uses mole ratios from the balanced equation to determine how many moles of one substance are needed, or produced, based on the amount of another substance. This principle is essential for ensuring that the proportions of reactants and products are correct in chemical calculations.

Mole Concept

The mole is a fundamental unit in chemistry that represents a specific number of particles, typically atoms or molecules. It allows chemists to convert between the mass of a substance and the number of entities present, providing a bridge between the macroscopic and microscopic worlds. This concept is crucial for quantifying the amounts of reactants or products in a chemical reaction.

Transcript

00:01 Hi there.

00:02 In this problem, i want to begin with a balanced equation.

00:06 We are making ammonia from its elements.

00:12 So nitrogen combines with hydrogen to make ammonia.

00:24 Balancing this equation would require a two ammonia and a three coefficient of three in front of the hydrogen.

00:33 Now that we have a balanced equation, let's see what we want to do in this problem.

00:39 We are trying to to make 9 .16 grams, i'm sorry, 9 .16 times 10 to the third grams of the ammonia.

00:56 And we want to know how many liters of nitrogen we need to start with to do that.

01:03 And the nitrogen is at a temperature of 575 celsius, 575 degrees celsius and a pressure of 248 atmospheres.

01:20 I'm going to go ahead and change this temperature to kelvin right away by adding 273, and that gives me 848 kelvin.

01:34 All right, so i have pulled everything out of the problem that i need to solve it.

01:39 We are given grams of the product so we can do some stoichiometry.

01:44 I can convert from grams of ammonia to molds of ammonia, and then use mold ratio to get me to moles of nitrogen.

01:51 At that point, however, i cannot use 22 .4 liters per mole because i am not at stp.

01:59 I'm not at standard temperature and pressure.

02:02 What i can do is use those moles and use the ideal gas equation to calculate the volume.

02:13 So that's my plan.

02:14 Let's go ahead and get started.

02:15 First thing is the stoichiometry, starting with the grams of the product that i'm trying to make.

02:29 First thing i need to do is divide by the molar mass to get to moles of ammonia.

02:35 The molar mass for ammonia is 17 .03 in every mole of ammonia.

02:53 This will allow me to cancel the units, grams of ammonia.

02:58 Now i'm ready to use the mole ratio from the balanced equation...

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