To find the volume of hydrogen gas produced when 14 grams of zinc metal reacts with sulfuric acid, you need to use the ideal gas law, which relates the amount of a gas to its volume under certain conditions. The ideal gas law is expressed as:
PV = nRT
Where:
- P is the pressure (which we'll assume is constant)
- V is the volume
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature in Kelvin
First, you need to find the number of moles of hydrogen gas produced. You can do this using the molar mass of zinc and the balanced chemical equation for the reaction between zinc and sulfuric acid:
Zn + H2SO4 -> ZnSO4 + H2
- The molar mass of zinc (Zn) is approximately 65.38 g/mol.
- The molar mass of hydrogen gas (H2) is approximately 2.02 g/mol.
Now, calculate the number of moles of zinc in 14 grams:
moles of Zn = mass / molar mass
moles of Zn = 14 g / 65.38 g/mol ≈ 0.214 mol
Since the balanced equation shows that one mole of zinc produces one mole of hydrogen gas, you have 0.214 moles of hydrogen gas.
Now, you can use the ideal gas law to find the volume of hydrogen gas:
PV = nRT
You'll need to know the temperature (T) and pressure (P) conditions to calculate the volume. Typically, this information is given in the problem or assumed to be standard conditions (0°C or 273.15 K and 1 atm).
Once you have the temperature and pressure, you can rearrange the ideal gas law to solve for volume (V):
V = (nRT) / P
Plug in the values and calculate the volume. Make sure to use consistent units throughout the calculation.