To calculate the moles of hydrogen gas (H2) produced, you'll typically use one of the following methods, depending on the information available:
1. Using the Ideal Gas Law
If you know the volume (V), pressure (P), and temperature (T) of the hydrogen gas, you can use the ideal gas law:
PV = nRT
Where:
- P = Pressure (in atmospheres, atm)
- V = Volume (in liters, L)
- n = Number of moles (what you want to find)
- R = Ideal gas constant (0.0821 L·atm/mol·K)
- T = Temperature (in Kelvin, K)
To solve for n (moles):
n = PV / RT
Example:
If you have 2.0 L of H2 gas at a pressure of 1.0 atm and a temperature of 273 K (standard temperature), then:
n = (1.0 atm 2.0 L) / (0.0821 L·atm/mol·K 273 K)
n ≈ 0.089 moles
2. Using Stoichiometry
If you know the amount of a reactant used or a product formed in a chemical reaction that produces hydrogen gas, you can use stoichiometry to determine the moles of H2 produced. You'll need a balanced chemical equation for this.
Example:
Consider the reaction of zinc (Zn) with hydrochloric acid (HCl):
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
If you react 65.38 g of Zn (which is 1 mole, since the molar mass of Zn is approximately 65.38 g/mol), according to the balanced equation, you will produce 1 mole of H2 gas.
If you use x moles of Zn, you will produce x moles of H2. You just need to convert the mass of Zn (or any other reactant or product) to moles using its molar mass, and then use the stoichiometric ratio from the balanced equation to find the moles of H2.
3. At Standard Temperature and Pressure (STP)
At STP (Standard Temperature and Pressure: 0°C or 273.15 K and 1 atm), one mole of any ideal gas occupies 22.4 liters. Therefore, if you know the volume of H2 gas at STP, you can calculate the moles:
n = V / 22.4 L/mol
Example:
If you have 44.8 L of H2 gas at STP:
n = 44.8 L / 22.4 L/mol = 2 moles
Summary
In summary, to calculate moles of hydrogen gas produced, use the ideal gas law if you know the pressure, volume, and temperature. Use stoichiometry if you know the amount of a reactant or product in a related chemical reaction. Use the molar volume at STP if you know the volume at standard temperature and pressure. Choose the method that best suits the available information.
