A sample of hydrogen was collected over water at `21^(@)C` and 685mm Hg. The volume of the container was 7.80 L. Calculate the mass of `H_(2)(g)` collected (vapour pressure of water = 18.6 mm Hg at `21^(@)C`)

Options

A. 0.283 g
B. 0.570g
C. 0.589 g
D. 7.14g

Answer

To solve the problem, we need to calculate the mass of hydrogen gas (H₂) collected over water at a given temperature and pressure. Here’s a step-by-step solution:

### Step 1: Determine the partial pressure of hydrogen gas (H₂)
The total pressure of the gas collected is the sum of the partial pressures of hydrogen and water vapor.

Given:
- Total pressure (P_total) = 685 mm Hg
- Vapor pressure of water at 21°C (P_water) = 18.6 mm Hg

Using Dalton's Law of Partial Pressures:
\[ P_{H_2} = P_{total} - P_{water} \]
\[ P_{H_2} = 685 \, \text{mm Hg} - 18.6 \, \text{mm Hg} = 666.4 \, \text{mm Hg} \]

### Step 2: Convert the partial pressure of hydrogen gas to atm
To use the ideal gas law, we need the pressure in atm.

Using the conversion factor \(1 \, \text{atm} = 760 \, \text{mm Hg}\):
\[ P_{H_2} = \frac{666.4 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} \approx 0.8768 \, \text{atm} \]

### Step 3: Use the ideal gas law to find the number of moles of H₂
The ideal gas law is given by:
\[ PV = nRT \]
Where:
- \(P\) = pressure in atm
- \(V\) = volume in liters
- \(n\) = number of moles
- \(R\) = ideal gas constant = 0.0821 L·atm/(K·mol)
- \(T\) = temperature in Kelvin

Convert the temperature from Celsius to Kelvin:
\[ T = 21 + 273 = 294 \, \text{K} \]

Now substituting the values into the ideal gas equation:
\[ n = \frac{PV}{RT} \]
\[ n = \frac{(0.8768 \, \text{atm})(7.80 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)})(294 \, \text{K})} \]

Calculating:
\[ n = \frac{6.84384}{24.2274} \approx 0.2833 \, \text{mol} \]

### Step 4: Calculate the mass of H₂
To find the mass, we use the molar mass of hydrogen gas (H₂), which is approximately 2 g/mol:
\[ \text{Mass} = n \times \text{Molar mass} \]
\[ \text{Mass} = 0.2833 \, \text{mol} \times 2 \, \text{g/mol} \approx 0.5666 \, \text{g} \]

### Final Answer
The mass of hydrogen gas collected is approximately **0.566 g**.

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