A sample of water gas contains 42% by volume of carbon monoxide. If the total pressure is 760 mm. the partial pressure of carbon monoxide is

Options

A. 380 mm
B. 319.2 mm
C. 38 mm
D. 360 mm

Answer

To find the partial pressure of carbon monoxide (CO) in a sample of water gas, we can follow these steps:

### Step 1: Understand the composition of water gas
Water gas is a mixture of carbon monoxide (CO) and hydrogen (H₂). According to the question, the sample contains 42% by volume of carbon monoxide.

### Step 2: Determine the volume of gases in the sample
If we consider a total volume of 100 mL of water gas:
- Volume of CO = 42% of 100 mL = 42 mL
- Volume of H₂ = 100 mL - 42 mL = 58 mL

### Step 3: Calculate the number of moles of each gas
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 liters (or 22400 mL). We can calculate the number of moles of CO and H₂ as follows:
- Number of moles of CO = Volume of CO / Molar volume = 42 mL / 22400 mL/mol = 0.001875 moles
- Number of moles of H₂ = Volume of H₂ / Molar volume = 58 mL / 22400 mL/mol = 0.002589 moles

### Step 4: Calculate the total number of moles
Total number of moles = Number of moles of CO + Number of moles of H₂
= 0.001875 moles + 0.002589 moles = 0.004464 moles

### Step 5: Calculate the mole fraction of carbon monoxide
Mole fraction of CO (x_CO) = Number of moles of CO / Total number of moles
= 0.001875 moles / 0.004464 moles = 0.420 (approximately)

### Step 6: Calculate the partial pressure of carbon monoxide
Using Dalton's Law of Partial Pressures, the partial pressure of CO can be calculated as:
Partial pressure of CO = Total pressure × Mole fraction of CO
= 760 mm × 0.420 = 319.2 mm

### Conclusion
The partial pressure of carbon monoxide in the sample of water gas is **319.2 mm**.

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