a sample of gas of unknown pressure occupies 0.766 L at the temperture of 298k the same sample of gas is than tested under known conditions and has the pressure of 32.6kPa and occupies 0.664 L at 303 k. What is the original pressure of gas
To find the original pressure of the gas, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure of the gas
V1 = Initial volume of the gas
T1 = Initial temperature of the gas
P2 = Final pressure of the gas
V2 = Final volume of the gas
T2 = Final temperature of the gas
Now we can plug in the given values into the equation:
(P1 * 0.766 L) / (298 K) = (32.6 kPa * 0.664 L) / (303 K)
To solve for P1, we can rearrange the equation:
P1 = (32.6 kPa * 0.664 L * 298 K) / (0.766 L * 303 K)
Now we can calculate:
P1 = (32.6 * 0.664 * 298) / (0.766 * 303)
P1 ≈ 22.87 kPa
Therefore, the original pressure of the gas is approximately 22.87 kPa.
To find the original pressure of the gas, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure of the gas (unknown)
V₁ = initial volume of the gas = 0.766 L
T₁ = initial temperature of the gas = 298 K
P₂ = final pressure of the gas = 32.6 kPa
V₂ = final volume of the gas = 0.664 L
T₂ = final temperature of the gas = 303 K
Let's plug in the given values into the equation:
(P₁ * 0.766) / (298) = (32.6 * 0.664) / (303)
To solve for P₁, we can cross multiply and then divide:
(P₁ * 0.766 * 303) = (32.6 * 0.664 * 298)
P₁ = (32.6 * 0.664 * 298) / (0.766 * 303)
Calculating the right side of the equation:
P₁ ≈ 18.361 kPa
Therefore, the original pressure of the gas is approximately 18.361 kPa.