What mass of hydrogen gas H2 at 0 °C and 1 atm could be contained in a vessel that holds 4.0 g of oxygen gas O2
at 0 °C and 1 atm?
the container has a volume of 4.0/32 = 1/8 mole of O2
Since the pressure and temperature are the same, the container will hold 1/8 mole of H2, or 0.25 g
To determine the mass of hydrogen gas, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, we need to find the number of moles of oxygen gas by using the ideal gas law equation. Given:
Pressure of oxygen gas (PO2) = 1 atm
Volume of vessel (VO2) = Unknown
Mass of oxygen gas (mO2) = 4.0 g
Molar mass of oxygen gas (MO2) = 32.00 g/mol (from periodic table)
Temperature (TO2) = 0 °C = 273.15 K (convert to Kelvin)
We know that:
nO2 = (mO2 / MO2)
Substituting the values:
nO2 = (4.0 g / 32.00 g/mol)
nO2 = 0.125 mol
Now, we can determine the volume of the vessel in order to calculate the number of moles of hydrogen gas using the same ideal gas law equation. Given:
Pressure of hydrogen gas (PH2) = 1 atm
Molar mass of hydrogen gas (MH2) = 2.02 g/mol (from periodic table)
Temperature (TH2) = 0 °C = 273.15 K (convert to Kelvin)
Number of moles of hydrogen gas (nH2) = Unknown
We know that:
PV = nRT
Solving for V:
VH2 = (nH2RT / PH2)
Since we want to find the mass of hydrogen gas, we need to find the number of moles of hydrogen gas:
nH2 = nO2 (according to the balanced chemical equation for the reaction)
Substituting the values:
VH2 = (0.125 mol * 0.0821 atm L / (mol K) * 273.15 K / 1 atm)
VH2 = 2.2225 L
Finally, to calculate the mass of hydrogen gas, we can use the molar mass of hydrogen gas and the obtained volume. Given:
Mass of hydrogen gas (mH2) = Unknown
We know that:
mH2 = (nH2 * MH2)
Substituting the values:
mH2 = (0.125 mol * 2.02 g/mol)
mH2 = 0.2525 g
Therefore, the mass of hydrogen gas that could be contained in the vessel is approximately 0.2525 grams.
To find the mass of hydrogen gas that could be contained in a vessel holding 4.0 g of oxygen gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (1 atm)
V = volume (unknown in this case)
n = amount of substance in moles of the gas (unknown in this case)
R = ideal gas constant (0.0821 L⋅atm/(mol⋅K))
T = temperature in Kelvin (0°C = 273.15 K)
We can start by finding the number of moles of oxygen gas using its mass and molar mass.
Step 1: Find the number of moles of oxygen gas (O2)
Given: Mass of oxygen gas (O2) = 4.0 g
Molar mass of oxygen gas (O2) = 32 g/mol
Number of moles of oxygen gas (O2) = Mass of oxygen gas (O2) / Molar mass of oxygen gas (O2)
= 4.0 g / 32 g/mol
= 0.125 mol
Now, we can use the stoichiometry of the balanced chemical equation that relates hydrogen gas (H2) to oxygen gas (O2) to find the number of moles of hydrogen gas.
Step 2: Use stoichiometry to find the number of moles of hydrogen gas (H2)
Given: The balanced chemical equation for the reaction between hydrogen gas (H2) and oxygen gas (O2) is 2H2 + O2 -> 2H2O
From the equation, we can see that every 1 mol of oxygen gas (O2) requires 2 moles of hydrogen gas (H2) to react.
Number of moles of hydrogen gas (H2) = 2 × Number of moles of oxygen gas (O2)
= 2 × 0.125 mol
= 0.25 mol
Finally, we can calculate the mass of hydrogen gas using its number of moles and molar mass.
Step 3: Calculate the mass of hydrogen gas (H2)
Given: Molar mass of hydrogen gas (H2) = 2 g/mol
Mass of hydrogen gas (H2) = Number of moles of hydrogen gas (H2) × Molar mass of hydrogen gas (H2)
= 0.25 mol × 2 g/mol
= 0.50 g
Therefore, the mass of hydrogen gas that could be contained in the vessel is 0.50 g at 0 °C and 1 atm.