# A 5 L container holds 12  mol and 6  mol of gasses A and B, respectively. Every four of molecules of gas B bind to three molecule of gas A and the reaction changes the temperature from 360^oK to 420 ^oK. By how much does the pressure change?

Aug 1, 2016

The pressure changed by: 2.39 × 10^6 Pa (to 3 sig figs)

#### Explanation:

To get started we’ll work out how many moles of gas are present at the end of the reaction, we start with 12 moles of gas A and 6 moles of gas B (a total of 18 moles). In the reaction gas A bonds with gas B at a ratio of 3:4 molecules, so that ratio will apply to the number of moles also.

There are only 6 moles of gas B which is not a multiple of 4, so only 4 moles of gas B will react and only 3 moles of gas A will react (due to 3:4 ratio). That gives only 1 mole of the new gas from the reaction. In the end we have 9 moles of gas A left, 2 moles of gas B and 1 mole of the new gas, a total of 12 moles.

Ideal Gas Equation
Use the ideal gas equation to find the pressure change: $p V = n R T$
p is pressure (Pa)
V is volume (m³)
n is number of moles (mol)
R is the molar gas constant (8.31 m² kg s⁻² K⁻¹ mol⁻¹)
T is temperature (K)

Here is the equation with pressure as the subject:
$p = \frac{n R T}{V}$
⇒ p_1 - p_2 = (n_1RT_1)/V_1 - (n_2RT_2)/V_2

The question implies that the volume does not change so ${V}_{1} = {V}_{2}$
⇒ p_1 - p_2 = ((n_1RT_1) - (n_2RT_2))/V

Before calculation the volume needs to be converted into cubic metres: V = 5L = 5×10^(-3) m³

Substitute in the values
⇒ p_1 - p_2 = ((18 × 8.31 × 360) - (12 × 8.31 × 420))/(5×10^(-3)) = 2.393 × 10^6 Pa

The pressure changed by:
2.39 × 10^6 Pa (to 3 sig figs)