Question

An ideal gas is contained in a cylinder with a volume of 5.5 x 10^2 mL at a temperature of 20.°C and a pressure of 700, torr. The gas is then compressed to a volume of 27 mL, and the temperature is raised to 810. C. What is the new pressure of the gas?

Answer 1

11,857.32 torr.

Step-by-step explanation:

To calculate the new pressure of the gas, we can use the combined gas law equation, which relates the initial and final states of an ideal gas.

The combined gas law equation is:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:

P1 and P2 are the initial and final pressures, respectively,

V1 and V2 are the initial and final volumes, respectively,

T1 and T2 are the initial and final temperatures in Kelvin, respectively.

Let's convert the given temperatures to Kelvin:

20.°C + 273.15 = 293.15 K (initial temperature)

810.°C + 273.15 = 1083.15 K (final temperature)

Now, let's substitute the given values into the combined gas law equation:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

(700 torr * 550 mL) / (293.15 K) = (P2 * 27 mL) / (1083.15 K)

Simplifying the equation:

(700 torr * 550 mL * 1083.15 K) = (P2 * 27 mL * 293.15 K)

Solving for P2 (the new pressure):

P2 = (700 torr * 550 mL * 1083.15 K) / (27 mL * 293.15 K)

P2 ≈ 11,857.32 torr

Therefore, the new pressure of the gas is approximately 11,857.32 torr.