50 cm 3 of gas was collected over water at 10ºC and 765 mm Hg. Calculate the volume of the gas at s.t.p. if…

To solve this problem, we use the Combined Gas Law, while accounting for the pressure of water vapor since the gas was collected over water.

1. Analyze the question

• Initial Volume ($V_1$): $50\text{ cm}^3$
• Initial Temperature ($T_1$): $10^\circ\text{C} = 10 + 273 = 283\text{ K}$
• Initial Pressure ($P_1$): The gas is collected over water, so the total pressure includes the pressure of the gas and the saturated vapour pressure (SVP) of water. • $P_{\text{gas}} = P_{\text{total}} - P_{\text{water vapor}}$ • $P_1 = 765\text{ mm Hg} - 5\text{ mm Hg} = 760\text{ mm Hg}$
• S.T.P. Conditions: • Standard Pressure ($P_2$): $760\text{ mm Hg}$ • Standard Temperature ($T_2$): $273\text{ K}$
• Target: Find $V_2$ (Volume at S.T.P.)

2. Explain the concept

The Combined Gas Law is expressed as:

When a gas is collected over water, it is "moist." To find the volume of the "dry" gas, we must subtract the vapour pressure of the water from the total atmospheric pressure.

3. Show the solution

Rearrange the formula to solve for $V_2$:

Substitute the values:

Notice that $760$ appears in both the numerator and the denominator, so they cancel out:

4. Identify the answer

Rounding to two decimal places, we get $48.23\text{ cm}^3$. This matches option D.

5. Exam Tip

Always remember that whenever you see "collected over water," you must subtract the S.V.P. from the total pressure before plugging the values into your gas law equations. Also, ensure your temperature is always converted to Kelvin by adding $273$.