Question

500 mL of nitrogen at $27^\circ C$ is cooled to $-5^\circ C$ at the same pressure. The new volume becomes

• A. 326.32 mL
• B. 446.66 mL
• C. 546.32 mL
• D. 771.56mL

Answer 1

The Correct Option is B

To find the new volume of nitrogen gas when it is cooled, we can use Charles's Law. Charles's Law is defined as:

\frac{V_1}{T_1} = \frac{V_2}{T_2}

where:

• V_1 = Initial volume = 500 mL
• T_1 = Initial temperature in Kelvin
• V_2 = Final volume
• T_2 = Final temperature in Kelvin

First, we need to convert the temperatures from Celsius to Kelvin, using the formula:

T(K) = T(°C) + 273.15

For the initial temperature:

• T_1 = 27^\circ C + 273.15 = 300.15 \, K

For the final temperature:

• T_2 = -5^\circ C + 273.15 = 268.15 \, K

Now, substituting the known values into Charles's Law, we get:

\frac{500 \, \text{mL}}{300.15 \, \text{K}} = \frac{V_2}{268.15 \, \text{K}}

To find V_2, we solve the above equation:

V_2 = \frac{500 \times 268.15}{300.15}

Calculating the above expression:

V_2 \approx 446.66 \, \text{mL}

Therefore, the new volume of nitrogen gas when cooled to -5^\circ C at constant pressure is approximately 446.66 mL.