What is the volume occupied by 8.0 g of hydrogen under a pressure of 2.8 atm and a temperature of 300 K?
To calculate the volume occupied by a gas, we can use the ideal gas law, which states:
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/K·mol)
T = temperature (in Kelvin)
In this case, we are given the pressure (P = 2.8 atm), the temperature (T = 300 K), and we need to find the volume (V) for a known mass of hydrogen (8.0 g). Here's how we can find the number of moles (n) of hydrogen:
1. Calculate the molar mass of hydrogen (H2):
The molar mass of hydrogen is 2 g/mol (1.0 g/mol for each H atom).
Since we have 8.0 g of hydrogen, we can calculate the number of moles using the formula:
Number of moles (n) = mass (m) / molar mass (M)
n = 8.0 g / 2 g/mol = 4.0 mol
2. Substitute the known values into the ideal gas law equation and solve for V:
PV = nRT
V = (nRT) / P
V = (4.0 mol * 0.0821 L·atm/K·mol * 300 K) / 2.8 atm
V ≈ 70.07 L
Therefore, the volume occupied by 8.0 g of hydrogen under a pressure of 2.8 atm and a temperature of 300 K is approximately 70.07 liters.