Gas Volume Calculation based on Temperature Change

How does the volume of a gas change when its temperature is lowered?

Given a fixed amount of gas held at constant pressure, calculate the volume (in L) it would occupy if a 3.50 L sample were cooled from 90.0°C to 30.0°C.

Answer:

The final volume of a gas originally occupying 3.50 L at 90.0°C when cooled to 30.0°C at constant pressure is 2.85 liters according to Charles's Law.

When a gas is cooled, its volume tends to decrease due to the decrease in temperature. This relationship between temperature and volume of a gas at constant pressure is described by Charles's Law, which states that the volume of a gas is directly proportional to its absolute temperature.

For the specific example provided, where a 3.50 L sample of gas is cooled from 90.0°C to 30.0°C, we can calculate the final volume using Charles's Law formula: V1/T1 = V2/T2.

First, we convert the temperatures to Kelvin:

• T1 = 90.0°C + 273.15 = 363.15 K
• T2 = 30.0°C + 273.15 = 303.15 K

Next, we substitute the initial volume (V1 = 3.50 L) and temperatures into the formula:

V2 = V1 × (T2/T1)

V2 = 3.50 L × (303.15 K / 363.15 K) = 2.85 L

Therefore, when the 3.50 L sample of gas is cooled from 90.0°C to 30.0°C, it would occupy a volume of 2.85 liters.