Question

In a storage area of a hospital where the temperature has reached 55°C, the pressure of oxygen gas in a 15.0-L steel cylinder is 965. What temperature, in degrees Celsius, would the gas have to be cooled to reduce the pressure to 850 torr when the volume and amount of gas don't change?

Options:
a. 50°C
b. 40°C
c. 35°C
d. 45°C

Answer 1

By plugging in the given values, we find that the temperature would have to be cooled to 45°C to reduce the pressure to 850 torr. Option D is correct.

Step-by-step explanation:

To solve this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. In this case, the volume and amount of gas do not change, so we can rearrange the equation to solve for T.

Since we are given the initial pressure, volume, and temperature, we can plug in those values into the equation and solve for n:

P₁V₁ = nRT₁

Solving for n:

n = (P₁V₁) / (R*T₁)

Once we have the number of moles, we can use it to find the final temperature using the rearranged ideal gas law equation:

P₂V₁ = nRT₂

Solving for T₂:

T₂ = (P₂V₁) / (nR)

Plugging in the given values, we have:

T₂ = (850 torr * 15.0 L) / ((965 torr * 15.0 L) / (55 °C + 273.15 K))

T₂ = 45 °C

So the correct answer is Option d. 45°C.