A sample of hydrogen chloride gas occupies 0.550L at STP. What is the pressure in atm if the volume is 7.50×10−2L at 20∘C?
(P1V1/T1) = (P2V2/T2)
P1 = 1
V1 = 0.550
T1 = 273
P2 = ?
V2 = 7.50E-2L
T2 = 273 + 20
To find the pressure in atm at a different condition, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
To solve this problem, you need to convert the given data into the correct units.
1. Convert the initial volume from 0.550L to the final volume at 20°C:
V1 = 0.550L
V2 = 7.50 x 10^-2 L
2. Convert the temperature from 20°C to Kelvin:
T = 20°C + 273.15 = 293.15 K
3. Since the compound is hydrogen chloride (HCl), the number of moles (n) can be calculated using the ideal gas law and the molar mass of hydrogen chloride. The molar mass of HCl is approximately 36.5 g/mol.
4. Convert the molar mass of HCl to kilograms:
molar mass = 36.5 g/mol
molar mass = 0.0365 kg/mol
5. Calculate the number of moles:
n = mass / molar mass
To find the mass of HCl gas, you can use its density at STP (Standard Temperature and Pressure). The density of HCl gas at STP is approximately 1.639 g/L, so you can calculate the mass using the initial volume:
mass = density x volume
mass = 1.639 g/L x 0.550 L
Now, plug in the values into the ideal gas law equation:
PV = nRT
P1V1 / T1 = P2V2 / T2
P2 = P1V1T2 / (V2T1)
Substitute the values:
P2 = (P1 x V1 x T2) / (V2 x T1)
P2 = (1 atm x 0.550 L x 293.15 K) / (7.50 x 10^-2 L x 273.15 K)
P2 ≈ 9.96 atm
Therefore, the pressure in atm if the volume is 7.50 x 10^-2 L at 20°C is approximately 9.96 atm.