What is the volume of 1.40 moles of nitrogen gas at 20.0°C and 770. torr?
To find the volume of 1.40 moles of nitrogen gas at 20.0°C and 770. torr, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20.0 + 273.15
T(K) = 293.15 K
Now, we can rearrange the ideal gas law equation to solve for the volume:
V = (nRT) / P
Substituting the given values:
V = (1.40 mol * 0.0821 L·atm/mol·K * 293.15 K) / 770. torr
Before we proceed, we should convert the pressure from torr to atm:
1 atm = 760. torr
So, the conversion factor is:
770. torr * (1 atm / 760. torr) = 1.01316 atm
Now, we can substitute the values and calculate the volume:
V = (1.40 * 0.0821 * 293.15) / 1.01316
V ≈ 34.57 L
Therefore, the volume of 1.40 moles of nitrogen gas at 20.0°C and 770. torr is approximately 34.57 liters.
To find the volume of 1.40 moles of nitrogen gas at 20.0°C and 770. torr, we need to use the ideal gas law equation, which is:
PV = nRT
Where:
- P is the pressure of the gas (in atm)
- V is the volume of the gas (in liters)
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 L.atm/mol.K)
- T is the temperature of the gas (in Kelvin)
First, let's convert the given pressure from 770. torr to atm (since the ideal gas constant is in atm units). We can use the conversion factor: 1 atm = 760 torr.
770. torr * (1 atm / 760 torr) = 1.0146 atm
Next, we need to convert the temperature from Celsius to Kelvin. To do this, we add 273.15 to the Celsius temperature.
20.0°C + 273.15 = 293.15 K
Now, we can plug these values into the ideal gas law equation and solve for V:
(1.0146 atm) * V = (1.40 mol) * (0.0821 L.atm/mol.K) * (293.15 K)
Simplifying:
V = (1.40 mol * 0.0821 L.atm/mol.K * 293.15 K) / 1.0146 atm
Calculating:
V ≈ 34.23 L
Therefore, the volume of 1.40 moles of nitrogen gas at 20.0°C and 770. torr is approximately 34.23 liters.