A sealed container holding 0.0255 L of an ideal gas at 0.989 atm and 71 °C is placed into a refrigerator and cooled to 45 °C with no change in volume. Calculate the final pressure of the gas.
the pressure is directly proportional to the absolute (Kelvin) temperature
Kelvin = Celsius + 273
p = .989 atm * [(45 + 273) / (71 + 273)]
Well, let's see if we can cool down that gas without making it too cool for school!
First, we need to convert those temperatures from Celsius to Kelvin. So, 71 °C + 273.15 = 344.15 K, and 45 °C + 273.15 = 318.15 K.
Now, 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 ideal gas constant, and T is the temperature in Kelvin.
Since the volume doesn't change, we can ignore it in this case. So we have P₁/T₁ = P₂/T₂, where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.
Plugging in the values, we get P₁/344.15 = P₂/318.15.
Now, solving for P₂, we find P₂ = P₁ * 318.15 / 344.15.
So, you just need to plug in the values of P₁ (0.989 atm) and calculate away!
But hey, don't worry about all those calculations. It's just gas under pressure trying to chill out in a fridge. Give it some time, and it'll find its final pressure in there!
To solve this problem, we can use the Combined Gas Law, which relates the initial and final temperature and pressure of a gas under constant volume:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = Initial pressure
V1 = Initial volume
T1 = Initial temperature
P2 = Final pressure (what we need to find)
V2 = Final volume (which remains the same in this case)
T2 = Final temperature
Let's organize the given values first:
P1 = 0.989 atm
V1 = 0.0255 L
T1 = 71 °C = 71 + 273.15 = 344.15 K
T2 = 45 °C = 45 + 273.15 = 318.15 K
Now we can substitute the values into the equation:
(0.989 atm * 0.0255 L) / 344.15 K = (P2 * 0.0255 L) / 318.15 K
Solving for P2:
(0.989 * 0.0255) / 344.15 = P2 / 318.15
P2 = (0.989 * 0.0255 * 318.15) / 344.15
P2 ≈ 0.911 atm
Therefore, the final pressure of the gas is approximately 0.911 atm.
To calculate the final pressure of the gas, we can use the Ideal Gas Law equation:
PV = nRT
where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the ideal gas constant, and
T is the temperature in Kelvin.
First, let's convert the given temperatures from Celsius to Kelvin.
Initial temperature, T1 = 71 °C = (71 + 273) K = 344 K
Final temperature, T2 = 45 °C = (45 + 273) K = 318 K
The volume remains constant, so V1 = V2 = 0.0255 L.
Next, we need to find the number of moles of gas.
To find the number of moles, we can use the ideal gas law equation and rearrange it to solve for n:
n = PV / RT
We already have P, V, and R.
We need to convert the given pressure from atm to Pa (Pascal) since R is in J/(mol·K).
1 atm = 101325 Pa
P1 = 0.989 atm = 0.989 * 101325 Pa = 100161.925 Pa
Now, we can calculate the number of moles:
n1 = P1 * V1 / (R * T1)
n2 = P2 * V2 / (R * T2)
Since V1 = V2, we can combine the formula:
n2 = P1 * V1 / (R * T1) * T2
Finally, we can calculate the final pressure using the number of moles and the final temperature:
P2 = n2 * R * T2 / V2
Substituting the values we found, we get:
P2 = [(P1 * V1 / (R * T1)) * T2] * R * T2 / V2
Now we can calculate the final pressure.