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The density of a gas a is twice that of ...

The density of a gas a is twice that of gas B. Molecular mass of A is half of the molecular of B. The ratio of the partial pressures of A and B is :

A

`1//4`

B

`1//2`

C

`4//1`

D

`2//1`

Text Solution

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To solve the problem, we need to find the ratio of the partial pressures of gases A and B given their densities and molecular masses. Let's break it down step by step. ### Step 1: Understand the relationship between density, molecular mass, and pressure The relationship between density (D), pressure (P), molecular mass (M), and temperature (T) for a gas is given by the formula: \[ P = \frac{D \cdot R \cdot T}{M} \] where R is the universal gas constant. ### Step 2: Define the variables based on the problem statement 1. Let \( D_A \) be the density of gas A. 2. Let \( D_B \) be the density of gas B. 3. Let \( M_A \) be the molecular mass of gas A. 4. Let \( M_B \) be the molecular mass of gas B. From the problem: - The density of gas A is twice that of gas B: \[ D_A = 2D_B \] - The molecular mass of gas A is half of the molecular mass of gas B: \[ M_A = \frac{1}{2} M_B \] ### Step 3: Express the partial pressures of gases A and B Using the formula for pressure: - For gas A: \[ P_A = \frac{D_A \cdot R \cdot T}{M_A} \] - For gas B: \[ P_B = \frac{D_B \cdot R \cdot T}{M_B} \] ### Step 4: Substitute the values of \( D_A \) and \( M_A \) in terms of \( D_B \) and \( M_B \) Substituting \( D_A = 2D_B \) and \( M_A = \frac{1}{2} M_B \) into the equations: - For gas A: \[ P_A = \frac{(2D_B) \cdot R \cdot T}{\frac{1}{2} M_B} = \frac{4D_B \cdot R \cdot T}{M_B} \] - For gas B: \[ P_B = \frac{D_B \cdot R \cdot T}{M_B} \] ### Step 5: Calculate the ratio of the partial pressures Now, we can find the ratio of the partial pressures: \[ \frac{P_A}{P_B} = \frac{\frac{4D_B \cdot R \cdot T}{M_B}}{\frac{D_B \cdot R \cdot T}{M_B}} = \frac{4D_B \cdot R \cdot T}{D_B \cdot R \cdot T} = 4 \] Therefore, the ratio of the partial pressures of gases A and B is: \[ \frac{P_A}{P_B} = 4:1 \] ### Final Answer The ratio of the partial pressures of A and B is \( 4:1 \). ---
To solve the problem, we need to find the ratio of the partial pressures of gases A and B given their densities and molecular masses. Let's break it down step by step. ### Step 1: Understand the relationship between density, molecular mass, and pressure The relationship between density (D), pressure (P), molecular mass (M), and temperature (T) for a gas is given by the formula: \[ P = \frac{D \cdot R \cdot T}{M} \] where R is the universal gas constant. ### Step 2: Define the variables based on the problem statement ...
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