A sample of ideal gas is in a sealed container. The pressure of the gas is 675torr , and the temperature is 28\, ^{\circ}C . If the temperature changes to 91\, ^{\circ}C with no change in volume or amount of gas, what is the new pressure, P_2, of the gas inside the container?
p₂=p₁T₂/T₁
p₁=675 torr = 89992.35 Pa
T ₁=273+28 =301 K
T₂ = 273+ 91= 364 K
To find the new pressure, P2, of the gas inside the container, we can use the combined gas law formula, which states:
(P1 × V1) / T1 = (P2 × V2) / T2
where P1 and P2 are the initial and final pressures of the gas, V1 and V2 are the initial and final volumes of the gas (which is not changing in this case), and T1 and T2 are the initial and final temperatures of the gas.
Given:
P1 = 675 torr
T1 = 28 °C = 28 + 273.15 K
T2 = 91 °C = 91 + 273.15 K
Since the volume and amount of gas remain constant, we can simplify the formula to:
P1 / T1 = P2 / T2
Now, let's plug in the given values:
P1 / T1 = P2 / T2
675 torr / (28 + 273.15 K) = P2 / (91 + 273.15 K)
Solving for P2:
675 torr / 301.15 K = P2 / 364.15 K
Cross-multiplying and simplifying:
P2 = (675 torr * 364.15 K) / 301.15 K
P2 ≈ 818.54 torr
Therefore, the new pressure, P2, of the gas inside the container is approximately 818.54 torr.