A sample of ideal gas is in a sealed container. The pressure of the gas is 615torr , and the temperature is 10 ∘ C . If the temperature changes to 56 ∘ C with no change in volume or amount of gas, what is the new pressure, P 2 , of the gas inside the container?
To find the new pressure of the gas, we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the initial temperature of 10 °C to Kelvin:
T1 = 10 °C + 273.15 = 283.15 K
Next, we can rearrange the ideal gas law equation to solve for the initial number of moles of gas:
n = PV / RT1
Substituting the given pressure of 615 torr (or 615 mmHg) and the temperature in Kelvin, we have:
n = (615 torr * V) / (0.0821 L∙atm/mol∙K * 283.15 K)
Now, let's find the new pressure of the gas when the temperature changes to 56 °C:
T2 = 56 °C + 273.15 = 329.15 K
Using the same number of moles (since there is no change in the amount of gas) and substituting the new temperature, we can find the new pressure:
P2 = (n * R * T2) / V
Substituting the value of n from the previous calculation and rearranging the equation, we get:
P2 = (615 torr * V * R * T2) / (615 torr * V * R * T1)
Simplifying the equation, we have:
P2 = (T2 / T1) * P1
Plugging in the values, we get:
P2 = (329.15 K / 283.15 K) * 615 torr
Now, we can calculate the new pressure:
P2 = 1.161 * 615 torr
P2 ≈ 714.38 torr
Therefore, the new pressure (P2) of the gas inside the container is approximately 714.38 torr.