Question

Consider 4.70 L of a gas at 365 mmHg and 20. ∘C . If the container is compressed to 2.40 L and the temperature is increased to 37 ∘C , what is the new pressure, P2 , inside the container? Assume no change in the amount of gas inside the cylinder.

Answer 1

P2 = 615 mmHg

Step-by-step explanation:

What we know:

• Initial volume (V1) = 4.70 L
• Initial pressure (P1) = 365 mmHg
• Initial temperature (T1) = 20°C
• Final volume (V2) = 2.40 L
• Final temperature (T2) = 37°C

What we need to find:

• Final pressure (P2)

Identify the gas law equation we can use. Here we can use Boyle's law:

• P1V1 = P2V2

Plug in the known values:
(365 mmHg)(4.70 L) = P2(2.40 L)

Solve for P2:

P2 = (365 mmHg)(4.70 L)/(2.40 L)

= 615 mmHg

Therefore, the final pressure inside the container is:

P2 = 615 mmHg

Answer 2

To find the new pressure, P2, inside the container, we can use the combined gas law formula:

P1V1/T1 = P2V2/T2

where P1 is the initial pressure, V1 is the initial volume, T1 is the initial temperature, P2 is the unknown pressure, V2 is the final volume, and T2 is the final temperature.

Given:
P1 = 365 mmHg
V1 = 4.70 L
T1 = 20 °C = 20 + 273.15 K
V2 = 2.40 L
T2 = 37 °C = 37 + 273.15 K

Now we can substitute these values into the formula and solve for P2:

(365 mmHg)(4.70 L)/(20 + 273.15 K) = P2(2.40 L)/(37 + 273.15 K)

First, let's convert the temperatures to Kelvin:

T1 = 20 + 273.15 K = 293.15 K
T2 = 37 + 273.15 K = 310.15 K

Substituting the values:

(365 mmHg)(4.70 L)/(293.15 K) = P2(2.40 L)/(310.15 K)

Now let's solve for P2:

365 mmHg * 4.70 L * 310.15 K = P2 * 2.40 L * 293.15 K

P2 = (365 mmHg * 4.70 L * 310.15 K)/(2.40 L * 293.15 K)

P2 = 3785.25 mmHg

Therefore, the new pressure, P2, inside the container is approximately 3785.25 mmHg.