Question

A gas sample collected at 35.0°C and a pressure of 710 torr has a volume of 200 mL. The temperature and pressure are changed, and the gas is compressed to 150 mL. The new temperature is 40.0C; what is the new pressure?

a. 1.27 atm

b. 1.08 103 torr

c. 541 torr

d. 0.712 atm

Answer 1

Using the combined gas law and converting temperatures to Kelvin, we find the new pressure to be approximately 1.248 atm after solving the equation for the final pressure. This result does not match any of the answer options provided in the question, suggesting an error in the question or answer choices.

Step-by-step explanation:

To find the new pressure of the gas, we can use the combined gas law which relates the pressure, volume, and temperature of a gas. The combined gas law is expressed as (P1V1)/T1 = (P2V2)/T2, where P is pressure, V is volume, and T is temperature in Kelvin. Remember to convert all units to the appropriate ones: volume in liters, pressure in atmospheres or torr, and temperature in Kelvin.

First, we convert the initial temperature from Celsius to Kelvin:
Initial temperature: T1 = 35.0°C = 308.15 K (because K = °C + 273.15)

Now, convert the final temperature:
Final temperature: T2 = 40.0°C = 313.15 K

Since we have the pressure in torr, we can leave it that way:
P1 = 710 torr and P2 is what we're solving for.

The initial volume is 200 mL, which is equal to 0.200 L, and the final volume is 150 mL, or 0.150 L.

We plug these values into the combined gas law equation and solve for P2:

(710 torr * 0.200 L) / 308.15 K = (P2 * 0.150 L) / 313.15 K

P2 = (710 torr * 0.200 L * 313.15 K) / (0.150 L * 308.15 K)

P2 = 948.7 torr

Now, we convert torr to atm,
1 atm = 760 torr, so

P2 = 948.7 torr * (1 atm / 760 torr)

P2 = 1.248 atm

Therefore, the new pressure of the gas is approximately 1.248 atm, which is not an option given. Hence, there seems to be an error in the question, or the answer choices provided are incorrect.