Question

Carbon dioxide is usually formed when gasoline is burned. If 30.0 L of CO₂ is produced at temperature of 1.00× 10³°C and allowed to reach room temperature (25.0°C) without any pressure changes, what is the new volume of the carbon dioxide?

Answer 1

The volume of CO₂ at a lower temperature can be found using Charles's Law. After converting the temperatures to Kelvin, the new volume is found to be approximately 7.03 liters.

Step-by-step explanation:

The question involves applying Charles's Law, which states that the volume of a gas is directly proportional to its temperature when the pressure is kept constant.

To determine the new volume of carbon dioxide (CO₂) when it cools from 1.00× 10³°C to room temperature (25.0°C), we convert all temperatures to the Kelvin scale and use the formula V1/T1 = V2/T2.

Firstly, convert the given temperatures to Kelvin:

• Initial temperature (T1) = 1.00 × 10³°C + 273.15 = 1273.15 K
• Final temperature (T2) = 25.0°C + 273.15 = 298.15 K

Given the initial volume (V1) is 30.0 L, we can rearrange the formula to find the new volume (V2): V2 = V1 × T2/T1.

Substitute the known values into the formula to calculate V2:

V2 = 30.0 L × (298.15 K / 1273.15 K) = 7.03 L (approximately)

Thus, the new volume of carbon dioxide at room temperature would be around 7.03 liters if the pressure remains unchanged.