Question

A volume of 160 cm3 of an ideal gas has an initial temperature of 20°C and an initial pressure of 1 atm. What is the final pressure if the volume is reduced to 115 cm3 and the temperature is raised to 40°C?

Answer 1

Using the combined gas law, the final pressure of the ideal gas when the volume is reduced to 115 cm3 and the temperature is raised to 40°C is approximately 1.393 atm.

Step-by-step explanation:

To find the final pressure of an ideal gas when the volume is reduced and the temperature is raised, we can use the combined gas law, which is expressed as P1V1/T1 = P2V2/T2, where P is pressure, V is volume, and T is temperature in Kelvin. We must first convert the temperatures from Celsius to Kelvin by adding 273 to each. Thus, we have T1 = 20°C + 273 = 293 K and T2 = 40°C + 273 = 313 K.

Now, we can insert the given values into the combined gas law equation:

1 atm × 160 cm3 / 293 K = P2 × 115 cm3 / 313 K

Let's solve for P2:

P2 = (1 atm × 160 cm3 / 293 K) × (313 K / 115 cm3)

P2 = (160 / 115) × (313 / 293) atm ≈ 1.393 atm

The final pressure of the gas when its volume is reduced to 115 cm3 and its temperature is increased to 40°C is approximately 1.393 atm.