At 22 degrees Celsius and 729 torr pressure, what will be the volume of 75 mol of NH3 gas?
PV = nRT
To find the volume of the NH3 gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in torr)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K or 62.36 L·torr/mol·K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 22 + 273.15
T(K) = 295.15 K
Using the given values:
P = 729 torr
n = 75 mol
R = 62.36 L·torr/mol·K
T = 295.15 K
Now we can calculate the volume (V) using the ideal gas law:
PV = nRT
V = (nRT) / P
V = (75 mol * 62.36 L·torr/mol·K * 295.15 K) / 729 torr
V = 18,261.45 L / 729
V ≈ 25.05 L
Therefore, at 22 degrees Celsius and 729 torr pressure, the volume of 75 mol of NH3 gas is approximately 25.05 liters.
To find the volume of the NH3 gas, we can use the ideal gas law equation: PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R represents the ideal gas constant, and T represents the temperature.
First, let's convert the given temperature from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature. Therefore, 22 degrees Celsius is equal to 22 + 273.15 = 295.15 Kelvin.
Next, use the given pressure, temperature, and number of moles to calculate the volume. The ideal gas constant (R) is 0.0821 L·atm/(mol·K).
1. Plug in the values into the ideal gas law equation:
PV = nRT
2. Substitute the given values:
(729 torr)·V = (75 mol)·(0.0821 L·atm/(mol·K))·(295.15 K)
3. Solve for V by rearranging the equation:
V = (75 mol)·(0.0821 L·atm/(mol·K))·(295.15 K) / (729 torr)
4. Convert torr to atmospheres (atm), as the ideal gas constant is given in L·atm/(mol·K):
1 atm = 760 torr
5. Convert the units and calculate the volume:
V = (75 mol)·(0.0821 L·atm/(mol·K))·(295.15 K) / (729 torr) * (1 atm / 760 torr)
Now, perform the calculations to find the volume of the NH3 gas.