Ideal Gas Law & Solutions (College Board AP® Chemistry)

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Written by: Martín

Reviewed by: Stewart Hird

Calculations of Gases & Solutions

Calculations with Ideal Gases

Gases that participate in chemical reactions can be used to perform mole calculations
It must be assumed that all the gasses behave as ideal gases
- Therefore, the ideal gas equation must be used depending on the context of the problem
The ideal gas equation connects the pressure (P), volume (V) and temperature (T) of an ideal gas with the amount of moles (n)
- The equation is shown below:

PV = nRT

The gas constant (R) can adopt different values depending on the units used for pressure, volume and temperature
- R = 8.314 J mol^-1 K^-1 = 0.08206 L atm mol^-1 K^-1 = 62.36 L torr mol^-1 K^-1
These values will be shown in the Equations and Constants section at the beginning of your AP Chemistry examination

Worked Example

The reaction of calcium carbonate (CaCO₃) and hydrochloric acid (HCl) produces calcium chloride (CaCl₂), water (H₂O), and carbon dioxide gas (CO₂). If the reaction takes place in a container at 1.02 atm and 27.0 ℃. How many liters of carbon dioxide are released when 50.0 g of sodium carbonate reacts with enough hydrochloric acid?

Answer:

Step 1: Write a balanced equation for the chemical reaction

CaCO₃ + HCl → CaCl₂ +H₂O + CO₂

Balance Cl

CaCO₃ + 2HCl → CaCl₂ +H₂O + CO₂

	Left	Right
Ca	1	1
C	1	1
O	3	3
H	2	2
Cl	2	2

The equation is balanced

Step 2: Analyze the statement and set up the steps that you are going to use to solve the problem. The initial quantity is always given by the statement

Step 3: Calculate the moles of calcium carbonate using its mass and molar mass

M = relative molecular mass of CaCO₃

M = (1 × mass of Ca) + (1 × mass of C) + (3 × mass of O)

M = (1 × 40.08) + (1 × 12.01) + (3 × 16.00)

M = 100.09 g mol^-1

n = m/M

n = 50.0 g/ 100.09 g mol^-1

n = 0.49955 mol of CaCO₃

Step 4: Calculate the moles of carbon dioxide using the ratio from the chemical equation

$0.49955 mol of {CaCO}_{3} \times \frac{1 mol of {CO}_{2}}{1 mol of {CaCO}_{3}} = 0.49955 mol of {CO}_{2}$

Since the ratio is 1:1 the moles of carbon dioxide must be the same

Step 5: Calculate the liters of carbon dioxide using the ideal gas equation

PV = nRT

Since the answer must be in liters, R = 0.08206 L atm mol^-1 K^-1

The pressure and temperature are given by the statement: 1.02 atm and 27.0 ℃ respectively

When working with the ideal gas equation, temperature must be in Kelvin. Therefore,

K = °C + 273

K = 27.0 + 273

K = 300 K

Once, temperature is in Kelvin and pressure in atm. The ideal gas equation can be applied

PV = nRT

Rearranging the equation,

$V = \frac{nRT}{P}$

Replacing the variables by the quantities given by the statement,

$V = \frac{(0.49955 mol) (0.08206 L atm {mol}^{- 1} K^{- 1}) (300 K)}{1.02 atm}$

V = 12.057 L

Step 6: Write the answer with the appropriate number of significant figures.

Since all the quantities from the statement are given with 3 significant figures. The answer must be written with 3 significant figures

The volume of carbon dioxide produced is 12.1 L

Calculation with Solutions

There are a lot of chemical reactions between solutions
- A solution is a liquid homogeneous mixture that has two components: a solute (in small amounts) a solvent (in big amounts)
- The solvent in most of the reaction is water
The amount of moles that are involved in the reaction depends on the concentration of the solution and its volume
Molarity (M) is used to quantify the concentration, and it connects the moles of solute (n) and the volume of solution in liters (V)

$M = \frac{n of solute}{V of solution in liters}$

Remember that L = dm³

Worked Example

How much L of 0.100 M KCl solution will react completely with 0.200 L of a 0.200 M Pb(NO₃)₂?

2KCl (aq) + Pb(NO₃)₂(aq) → PbCl₂(aq)+ 2KNO₃ (aq)

Answer:

Step 1: Analyze the statement and set up the steps that you are going to use to solve the problem. The initial quantity is always given by the statement. In calculations with solutions, start always with the reactant or product that you have the most information

Since, volume and molarity are given for Pb(NO₃)₂, it must be the starting point

calculations-with-solutions-worked-example

Step 2: Calculate the moles of Pb(NO₃)₂ using the molarity equation

$M = \frac{n of solute}{V of solution in liters}$

Rearranging the equation,

n of solute = M × V of solution in liters

Replacing the values,

n of solute = 0.200 M × 0.200 L

n of solute = 0.04 mol of Pb(NO₃)₂

Step 3: Calculate the moles of KCl that reacted using the ratio from the chemical equation

$0.04 mol of Pb ({NO}_{3})_{2} \times \frac{2 mol of KCl}{1 mol of Pb ({NO}_{3})_{2}} = 0.08 mol of KCl$

Since the ratio is 1:2 the moles of KCl must be double

Step 4: Calculate the volume in L of KCl solution that are needed to react completely

$M = \frac{n of solute}{V of solution in liters}$

Rearranging the equation,

$V of solution in liters = \frac{n of solute}{M}$

Replacing the values,

$V of solution in liters = \frac{0.08 mol of KCl}{0.100 M}$

$V of solution in liters = 0.8 L$

Step 5: Write the answer with the appropriate number of significant figures

Since all the quantities from the statement are given with 3 significant figures. The answer must be written with 3 significant figures

The volume of KCl solution required to react completely with the Pb(NO₃)₂ solution is 0.800 L

Last updated: 24 August 2024

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Ideal Gas Law & Solutions (College Board AP® Chemistry)

Study Guide

Calculations of Gases & Solutions

Calculations with Ideal Gases

Worked Example

Calculation with Solutions

Worked Example

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Author: Martín

Author: Stewart Hird