Question

Butane gas burns in air according to the following reaction,
$2{C_4}{H_{10}} + 13{O_2} \to 10{H_2}O + 8C{O_2}$
Suppose the initial and final temperatures are equal and high enough so that all reactants and products act as perfect gases. Two moles of butane are mixed with 13 moles of oxygen and then completely reached. Find the final pressure (if the volume remains unchanged and the pressure before the reaction is ${P_0}$ )?

Answer 1

Hint: We may use an ideal gas equation which is PV = nRT, where P = pressure of gases, V = volume occupied by gases, n = total moles of gases, R = gas constant, T = temperature of system.
Use the above equation in both cases, initially and finally, and then, we can get pressure by comparing.

Complete step by step answer:
Given,
Temperature is the same initially and finally.
\[{T_i} = {T_f} = T\]
Initial total moles = 2 + 13 = 15 moles
\[{n_i} = 15moles\]
To calculate final moles, we have to look at the equation. In a balanced chemical equation, the reaction takes place according to coefficients in the reaction.
Here we have been given 2 moles of butane reacting with 13 moles of oxygen, and the same number are coefficients in the given reaction, so the coefficient number of moles of products will be formed.
Thus 10 moles of water and 8 moles of Carbon dioxide will be formed.
${n_f} = 10 + 8 = 18moles$
Initial pressure = ${P_0}$ , Final pressure = ${P_f}$
Volume initially and finally is the same.
\[{V_i} = {V_f} = V\] litres
R is gas constant, which does not change at any situation.
Now let us substitute all initial values in ideal gas equation, we get:
\[{P_0}V = 15RT\] --- equation 1
Substitute all final values in ideal gas equation, we get:
\[{P_f}V = 18RT\] ---- equation 2
Divide equation 2 from equation 1,
We get,
\[\dfrac{{{P_f}}}{{{P_0}}} = \dfrac{{18}}{{15}} \\
\dfrac{{{P_f}}}{{{P_0}}} = \dfrac{6}{5} \\
{P_f} = \dfrac{6}{5}{P_0} \\\]

Note: Balancing of equations is essential, and in the balanced equation the coefficients will give us the number of moles reacting and number of moles of products formed.
From the ideal gas equation, PV = nRT , when we want to study the relationship of 2 things, while others are constant.