The mass of water vapour in a given volume of air is 0.05g at 20°C, while the mass of water vapour required to…

1. Analyze the question

We are asked to calculate the relative humidity of a sample of air. We are given:

• Mass of water vapour present (actual mass): $0.05\text{ g}$
• Mass of water vapour required to saturate the air (saturated mass): $0.15\text{ g}$

2. Explain the concept

Relative Humidity (RH) is defined as the ratio of the actual mass of water vapour present in a given volume of air to the mass of water vapour required to saturate the same volume of air at the same temperature. It is usually expressed as a percentage.

The formula is:

3. Show the solution

• Step 1: Identify the given values. • Actual mass = $0.05\text{ g}$ • Saturated mass = $0.15\text{ g}$

• Step 2: Substitute the values into the formula. $$\text{RH} = \left( \frac{0.05}{0.15} \right) \times 100\%$$

• Step 3: Simplify the fraction. $$\frac{0.05}{0.15} = \frac{5}{15} = \frac{1}{3}$$

• Step 4: Calculate the final percentage. $$\text{RH} = \frac{1}{3} \times 100\%$$ $$\text{RH} = 33.333...\%$$

Rounding to two decimal places, we get 33.33%.

4. Identify the answer

Comparing our result to the given options: A. 3.33% B. 5.55% C. 33.33% D. 55.55%

The correct option is C.

5. Tip

When calculating relative humidity, always remember that the "saturated" value must be the larger number (the denominator). If you ever get a percentage greater than 100%, you have likely swapped the numerator and the denominator! Also, remember that relative humidity is a ratio, so the units (grams) cancel out, leaving you with a dimensionless percentage.