a sample of gas has a volume of 500 ml at a pressure of 640torr. that volume in liters will the gas occupy at 1.00 atm pressure and constant temperature
P1V1 = P2V2
To find out the volume of the gas at a different pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature
Given the initial volume (500 mL) and pressure (640 torr), we need to convert them to the proper units before we can solve the equation.
1 atm = 760torr
1 L = 1000 mL
Converting the initial volume and pressure:
Volume = 500 mL = 500/1000 L = 0.5 L
Pressure = 640 torr
We are given that the temperature is constant, so we can consider it to be the same in both cases.
Now let's find the number of moles (n) using the ideal gas law equation with the initial conditions:
PV = nRT
(640 torr)(0.5 L) = n(0.0821 L·atm/mol·K)(T)
Since the temperature is constant, we can assume it cancels out on both sides of the equation:
(640 torr)(0.5 L) = n(0.0821 L·atm/mol·K)
Now, let's find n:
(640 torr)(0.5 L) / (0.0821 L·atm/mol·K) = n
n ≈ 3.108 moles
Now, we can use the new pressure and number of moles to calculate the volume using the ideal gas law equation:
PV = nRT
(1.00 atm)V = (3.108 mol)(0.0821 L·atm/mol·K)(T)
Again, since the temperature is constant, we can assume it cancels out:
(1.00 atm)V = (3.108 mol)(0.0821 L·atm/mol·K)
Now, let's solve for V:
V = (3.108 mol)(0.0821 L·atm/mol·K) / (1.00 atm)
V ≈ 0.255 L
Therefore, the gas will occupy a volume of approximately 0.255 liters under a pressure of 1.00 atm.