A sample of ammonia gas occupies a volume of 1.58 L at 22°C and a pressure of 0.983 atm. What volume will the sample occupy at 1.00 atm and 0°C? (K = oC + 273)
Use (P1V1/T1) = (P2V2/T2). Remember T must be in kelvin. Post your work if you get stuck.
To solve this problem, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, let's calculate the number of moles of ammonia gas in the initial sample. We can use the ideal gas law with the given conditions:
P1 = 0.983 atm (initial pressure)
V1 = 1.58 L (initial volume)
T1 = 22°C + 273 = 295 K (initial temperature)
We need to convert the temperature to Kelvin because the gas constant is given in units of atm·L/(mol·K).
Solving the ideal gas law equation for n:
n = (P1 * V1) / (R * T1)
Next, we can use the molar volume concept to calculate the final volume. The molar volume is the volume occupied by one mole of any gas at a specified temperature and pressure. At STP (standard temperature and pressure), which is 0°C and 1.00 atm, the molar volume is 22.4 L/mol.
So, we can set up a ratio:
(V1 / n1) = (V2 / n2)
Since we want to find V2, the final volume, we can rearrange the equation:
V2 = (V1 * n2) / n1
Now, we need to find n2, the number of moles at the new conditions. We can use the ideal gas law again:
P2 = 1.00 atm (new pressure at 0°C)
T2 = 0°C + 273 = 273 K (new temperature)
Using the ideal gas law:
n2 = (P2 * V1) / (R * T2)
Finally, substitute the values into the equation:
V2 = (V1 * n2) / n1
Now you can calculate the final volume V2.