A 250 mL sample of gas at 1.00 atm and 20oC has the temperature changed to 40oC and the volume changed to 500 mL. What is the new pressure?
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin
To find the new pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = gas constant
T = temperature in Kelvin
First, we need to convert the temperatures from Celsius to Kelvin. To do that, we add 273.15 to each temperature value.
Initial temperature: 20°C + 273.15 = 293.15 K
Final temperature: 40°C + 273.15 = 313.15 K
Next, we substitute the known values into the ideal gas law equation.
Initial pressure: 1.00 atm
Initial volume: 250 mL = 0.25 L (since 1 L = 1000 mL)
Initial temperature: 293.15 K
Final volume: 500 mL = 0.5 L
Final temperature: 313.15 K
Now, we can set up the initial and final equations:
Initial equation: (1.00 atm) × (0.25 L) = n × (0.0821 L·atm/mol·K) × (293.15 K)
Final equation: P × (0.5 L) = n × (0.0821 L·atm/mol·K) × (313.15 K)
Since the number of moles (n) stays the same, we can set the initial and final equations equal to each other:
(1.00 atm) × (0.25 L) = P × (0.5 L)
Now we can solve for the new pressure (P):
P = (1.00 atm) × (0.25 L) / (0.5 L)
P = 0.50 atm
Therefore, the new pressure is 0.50 atm.