Question

A sample of helium has a volume of 300. mL at 20.0°C. What is the temperature (°C) if the gas expands to 650. mL? (Pressure is constant)

A) 20.0°C
B) 10.0°C
C) 5.0°C
D) 0.0°C

Answer 1

Using Charles's Law, which states that the volume of a gas is directly proportional to its Kelvin temperature, the final temperature for helium gas to expand from 300 mL to 650 mL at constant pressure would be approximately 361.575°C. None of the provided options are correct.

Step-by-step explanation:

The question you have asked relates to how the temperature of a gas affects its volume, assuming pressure is constant, which is described by Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its Kelvin temperature as long as the pressure is held constant. To solve this problem, we need to use the formula derived from Charles's Law:

V1 / T1 = V2 / T2,

where V1 is the initial volume, T1 is the initial temperature in Kelvin, V2 is the final volume, and T2 is the final temperature in Kelvin. Remember to convert the temperatures from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Let's apply the formula:

1. Convert the initial temperature from Celsius to Kelvin: T1 = 20.0 + 273.15 = 293.15 K.
2. Insert the known quantities into the formula: 300 mL / 293.15 K = 650 mL / T2.
3. Solve for T2: T2 = (650 mL * 293.15 K) / 300 mL.
4. Calculate T2: T2 = 634.725 K.
5. Convert the final temperature back to Celsius: T2 - 273.15 = 634.725 K - 273.15 = 361.575°C.

So, the temperature would need to be approximately 361.575°C for the helium gas to expand from 300 mL to 650 mL at constant pressure. This result indicates that none of the options A) 20.0°C, B) 10.0°C, C) 5.0°C, D) 0.0°C is correct, as they all represent a temperature that is too low.