7. A container of He gas has a pressure of 1.2 atm, a volume of 320 mL, and a
temperature of 300 K. If the temperature increases to 350 K, and the volume is changed
to 400 mL, what is the new pressure?
To find the new pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
We can rearrange the equation to solve for P:
P = (nRT) / V
First, we need to calculate the initial number of moles of He gas using the initial conditions. We can use the formula:
n = PV / RT
Given:
P1 = 1.2 atm
V1 = 320 mL = 0.320 L
T1 = 300 K
R = 0.0821 L*atm/(mol*K)
n1 = (1.2 atm * 0.320 L) / (0.0821 L*atm/(mol*K) * 300 K)
n1 = 0.0156 mol
Using the initial number of moles, we can calculate the new pressure using the new conditions:
Given:
n2 = 0.0156 mol (since the number of moles does not change)
V2 = 400 mL = 0.400 L
T2 = 350 K
P2 = (n2 * R * T2) / V2
P2 = (0.0156 mol * 0.0821 L*atm/(mol*K) * 350 K) / 0.400 L
P2 = 0.0961 atm
Therefore, the new pressure is 0.0961 atm.