To solve this problem, we need to use the ideal gas law equation, which is given as follows:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of the gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
To find the volume of H2 gas, we need to determine the number of moles of H2 gas produced.
Step 1: Convert the temperature from Celsius to Kelvin.
Given: T = 23 °C
To convert to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
T(K) = 23 + 273.15
T(K) = 296.15K
Step 2: Convert the pressure from torr to atm.
Given: P = 678 torr
To convert to atm, we use the conversion factor:
1 atm = 760 torr
P(atm) = P(torr) / 760
P(atm) = 678 / 760
P(atm) = 0.8921 atm
Step 3: Calculate the number of moles of H2 gas produced.
Since the stoichiometry of the balanced equation tells us that 1 mole of zinc metal produces 1 mole of H2 gas, we need to calculate the number of moles of zinc metal first.
Given: Mass of zinc (Zn) = 7.59 g
Atomic mass of zinc (Zn) = 65.38 g/mol (from the periodic table)
n(Zn) = Mass(Zn) / Molar mass(Zn)
n(Zn) = 7.59 g / 65.38 g/mol
n(Zn) ≈ 0.116 mol
Since 1 mole of zinc (Zn) produces 1 mole of H2 gas, the number of moles of H2 gas produced is also 0.116 mol.
Step 4: Substitute the given values into the ideal gas law equation to find the volume (V) of H2 gas.
PV = nRT
V = (nRT) / P
Substituting the known values:
V = (0.116 mol * 0.0821 L.atm/mol.K * 296.15K) / 0.8921 atm
V ≈ 3.85 L
Therefore, the volume of H2 gas obtained is approximately 3.85 liters.