Question

which of the following is the formula to calculate the partial pressure of a gas in a mixture?
a. ( p _ { \text { gas } } = chi _ { \text { gas } } \times p _ { \text { total } } )
b. ( p _ { \text { gas } } = \frac { p _ { \text { total } } } { chi _ { \text { gas } } } )
c. ( p _ { \text { gas } } = v _ { \text { gas } } \times t _ { \text { total } } )
d. ( p _ { \text { gas } } = \frac { n _ { \text { gas } } } { p _ { \text { total } } } )

Explanation:

Step1: Recall Dalton's Law of Partial Pressures

According to Dalton's law, the partial pressure \(P_{\text{gas}}\) of a gas in a mixture is given by the mole - fraction \(X_{\text{gas}}\) of the gas multiplied by the total pressure \(P_{\text{total}}\) of the mixture.

Step2: Analyze each option

• Option a: \(P_{\text{gas}}=X_{\text{gas}}\times P_{\text{total}}\) is the correct formula for partial pressure.
• Option b: \(P_{\text{gas}}=\frac{P_{\text{total}}}{X_{\text{gas}}}\) is incorrect. If we re - arrange \(P = X\times P_{\text{total}}\) (where \(P = P_{\text{gas}}\)), we get \(X=\frac{P}{P_{\text{total}}}\), not this formula.
• Option c: \(P_{\text{gas}}=V_{\text{gas}}\times T_{\text{total}}\) has no relation to the formula for partial pressure. There is no such formula in the context of partial pressures (Dalton's law).
• Option d: \(P_{\text{gas}}=\frac{P_{\text{total}}}{n_{\text{gas}}}\) is incorrect. The mole - fraction \(X=\frac{n_{\text{gas}}}{n_{\text{total}}}\), and from \(P = X\times P_{\text{total}}\), we have \(P=\frac{n_{\text{gas}}}{n_{\text{total}}}\times P_{\text{total}}\), not this formula.

Answer:

A. \(P_{\text{gas}} = X_{\text{gas}}\times P_{\text{total}}\)