A mixture containing 4.33 g of CO2 and 3.11 g of CH4 has a total pressure of 1.09 atm

Step 1 of 2

Dalton's law of partial pressures: It  states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

Partial pressure can be calculated by using ideal gas equation if we assume that each gas acts independently.

Therefore, From the ideal gas equation,

 PV = nRT

\(\Rightarrow P_{n}=n_{n} R T / V \dots \dots (1)\)

Therefore, when a mixture contain multi component, then the partial pressure of each component would be.

\(\begin{aligned}
P_{a} & =n_{a} R T / V \ldots \ldots \ldots(2) \\
P_{b} & =n_{b} R T / V \ldots \ldots .
\end{aligned}\)

Thus, total pressure 

\(P=P_{a}+P_{b}+\ldots \ldots\)

\(\begin{array}{l}
=R T / V\left(n_{a}+n_{b}+\ldots . .\right) \\
=n_{n} R T / V \ldots \ldots \ldots(3)
\end{array}\)

Since,

Divide the equation (2) by equation (3)  we get

\(\frac{P a}{P}=\frac{n a(R T / V)}{n n R T / V}=\mathrm{n}_{\mathrm{a}} / \mathrm{n}_{\mathrm{n}} \dots (4)\)