Using the same sample of gas (P 1 = 615torr , T 1 = 10 ∘ C ), we wish to change the pressure to 6150torr with no accompanying change in volume or amount of gas. What temperature T 2 , in Celsius, is needed to reach this pressure?
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure
V is the volume
n is the amount of gas (constant in this case)
R is the ideal gas constant
T is the temperature
Since the volume and amount of gas are constant, we can rewrite the equation as:
P/T = constant
Now, let's solve for the unknown temperature T₂.
First, we'll set up the equation using the initial conditions (P₁ = 615 torr and T₁ = 10 °C):
P₁/T₁ = P₂/T₂
Substituting the given values, we have:
615 torr / (10 + 273.15 K) = 6150 torr / T₂
Now, we can solve for T₂:
T₂ = (6150 torr * (10 + 273.15 K)) / 615 torr
T₂ ≈ 337.15 K
To convert this temperature to Celsius, subtract 273.15:
T₂ ≈ 64 °C
Therefore, a temperature of approximately 64 °C is needed to reach a pressure of 6150 torr, assuming no change in volume or amount of gas.