Question

How would you calculate the partial pressure of $C{O_2}$, given an atmospheric pressure of ${\text{760 mm Hg}}$ and a {\text{0}} \cdot {\text{04% }} concentration?

Answer 1

Analyze the given values in the question itself. Each component which is present in a gaseous mixture is dependent on the total pressure which is exerted by the mixture to the number of molecules that are present in the mixture.

Complete step by step answer: 1) First of all we will see the formula for the partial pressure of gas which is being expressed in terms of mole fraction as below,
${P_{gas}} = x{_{gas}} \times {P_{mixture}}$
In the above equation, ${x_{gas}} =$ Mole fraction of gas
${P_{mixture}} =$ The pressure exerted by the gas
The above formula shows proportionality to the number of molecules.
2) Now as we know that one mole of any substance is equal to the exact $6 \cdot 023 \times {10^{23}}$ molecules of that substance and this number is known as Avogadro’s number that is ${N_A}$.
3) Now let us see an expression for the number of moles of gas by using the number of molecules, suppose say x,
${\text{Number of moles = Number of molecules }} \times {\text{ }}{{\text{N}}_A}$
4) Now, the percent composition value of a gaseous mixture elaborates how many molecules each gas contributes to ${\text{100}}$ molecules of the mixture. In this question, the air is said to be $0 \cdot 04\%$ carbon dioxide. This also means that in every ${\text{100}}$ molecule of air, ${\text{0}} \cdot {\text{04}}$ will be $C{O_2}$ molecules. This can be expressed in the formula as below,
${n_{C{O_2}}} = 0 \cdot 04{\text{ molecules }} \times {\text{ }}{{\text{N}}_A}$
Now, the Total number of moles in the sample air will be,
${n_{Total}} = 100 \times {N_A}$
5) Now, this means that the mole fraction of carbon dioxide in the mixture can be calculated as below,
${x_{C{O_2}}} = \dfrac{{0 \cdot 4 \times {N_A}}}{{100 \times {N_A}}} = 0 \cdot 00004$
6) Now we need Carbon dioxide’s partial pressure in the air which will be,
${P_{C{O_2}}} = 0 \cdot 00004 \times 760mmHg = 0 \cdot 304mmHg$
Therefore, the partial pressure $C{O_2}$ is $0 \cdot 304mmHg$.

Note:
The partial pressure is the term that is used for the measurement of the thermodynamic activity of gas molecules. The reaction between the gases happens according to their individual partial pressure and not on the concentration of gases in a gaseous mixture.