Question

The gas inside a 42.5 mL piston has a temperature of 21°C. If the temperature is lowered to -21°C, what is the new volume of the gas? Show all your work.

Answer 1

To find the new volume of gas, we can use the ideal gas law equation PV = nRT. Given the initial volume and temperature, and the final temperature, we can calculate the final volume using the equation V2 = V1 * T2 / T1.

Step-by-step explanation:

To solve this problem, we can use the ideal gas law equation, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

Since the pressure remains constant, we can use the equation PV = nRT to find the final volume. The initial volume (V1) is given as 42.5 mL, and the initial temperature (T1) is 21°C. We need to convert the temperatures to Kelvin by adding 273.15 to each value.

So, V1 = 42.5 mL and T1 = 21 + 273.15 = 294.15 K. The final temperature (T2) is -21°C, which is -21 + 273.15 = 252.15 K. Now we can solve for the final volume (V2) by rearranging the equation:

V2 = V1 * T2 / T1

Plugging in the values, V2 = 42.5 mL * 252.15 K / 294.15 K.

Calculating the final volume gives us V2 = 36.520 mL.