calculate the volume occupied by 5.25 gram of nitrogen at 26 degree Celsius and 74.2 cm of pressure
To calculate the volume of a gas, you can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
First, let's convert the given temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 26 + 273.15
T(K) = 299.15 K
Next, convert the given pressure from cm of Hg to atm:
1 atm = 76 cm of Hg
P(atm) = P(cm of Hg) / 76
P(atm) = 74.2 / 76
P(atm) = 0.974 atm
Now, to find the number of moles (n) of nitrogen gas, we can use the molar mass of nitrogen (28.0134 g/mol):
n = mass / molar mass
n = 5.25 g / 28.0134 g/mol
n ≈ 0.187 mol
Now we have all the values we need to calculate the volume (V):
V = (nRT) / P
V = (0.187 mol) * (0.0821 L·atm/mol·K) * (299.15 K) / (0.974 atm)
V ≈ 4.86 L
Therefore, the volume occupied by 5.25 grams of nitrogen gas at 26 degrees Celsius and 74.2 cm of pressure is approximately 4.86 liters.
Assuming 74.2 cm of pressure refers to the mercury column.
Under standard temperature and pressure (273.15°K, 100 kPa=760.06 mmHg),
the gas constant is:
62.364 L mmHg K−1 mol−1
molecular mass of N2=2*14.0067=28.0134
So
volume occupied by 5.25 gram of nitrogen at 26 degree Celsius and 74.2 cm of pressure
=62.364/742*(273.15+26)*(5.25/28.0134)
=4.7 litres