Question

A gas occupies a volume of 140 mL at 35.0°C and 97 kPa. What is the volume of the gas at 0ºC and 101 kPa? Show all your work.

Answer 1

The volume of the gas at 0°C and 101 kPa, calculated using the combined gas law, is approximately 119 mL.

Step-by-step explanation:

To calculate the volume of the gas at 0°C and 101 kPa, we must apply the combined gas law: P1V1/T1 = P2V2/T2. This equation compares the initial state (P1, V1, T1) with the final state (P2, V2, T2), factoring pressure (P), volume (V), and temperature (T).

First, we need to convert the temperatures from Celsius to Kelvin by adding 273.15. So 35.0°C becomes 308.15 K, and 0°C becomes 273.15 K.

Next, we plug our values into the combined gas law:

• P1 = 97 kPa
• V1 = 140 mL
• T1 = 308.15 K
• P2 = 101 kPa
• V2 is what we're solving for
• T2 = 273.15 K

Substituting the values into the equation:

97 kPa * 140 mL / 308.15 K = 101 kPa * V2 / 273.15 K

We can simplify this to find V2:

V2 = (97 kPa * 140 mL * 273.15 K) / (308.15 K * 101 kPa)

By calculating, the final volume V2 comes out to approximately 119 mL.