SHOW WORK
A cylinder contains 36.5g of argon gas at a pressure of 8.20atm. The valve is opened and gas is allowed to escape until the pressure is reduced to 4.75atm at constant temperature. How many grams of argon escaped?
See your previous problems.
kek
To solve this problem, we need to make use of the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, the temperature is constant, so we don't need to consider it in our calculations.
We are given:
P1 = 8.20 atm
P2 = 4.75 atm
To find the number of moles of argon gas, we need to find the initial and final volume.
Assuming the cylinder is rigid, the volume will be constant, and we can write the equation as:
P1V1 = P2V2
Rearranging the equation to solve for V2:
V2 = (P1V1) / P2
Now, let's calculate the volume:
V2 = (8.20 atm * V1) / 4.75 atm
Next, we need to find the number of moles in the cylinder before and after the gas has escaped.
Using the ideal gas law equation, we can write:
P1V1 = n1RT
P2V2 = n2RT
Since the temperature is constant, we can assume R is constant as well. Therefore, we can write:
P1V1 = n1
P2V2 = n2
Substituting the values we have:
P1V1 = n1
4.75 atm * V2 = n2
Now, let's find the initial number of moles of argon gas:
n1 = P1V1 = (8.20 atm) * V1
Next, let's find the final number of moles of argon gas:
n2 = 4.75 atm * V2
Finally, to find the grams of argon gas that escaped, we need to subtract the final number of moles from the initial number of moles and convert it to grams:
grams of argon escaped = (n1 - n2) * molar mass of argon
The molar mass of argon is approximately 39.95 g/mol.
So to complete the calculations, you need to know the initial volume of the cylinder (V1). With that information, you can find the final volume (V2), the initial number of moles (n1), the final number of moles (n2), and then calculate the grams of argon gas that escaped.