Final answer:
To find the volume of hydrogen gas produced, calculate moles of gallium used, convert them to moles of hydrogen based on stoichiometry, and then apply the ideal gas law with the given temperature and pressure to find the volume.
Step-by-step explanation:
To calculate the volume of hydrogen gas produced from the reaction of gallium with hydrochloric acid, we must use stoichiometry and the ideal gas law. The reaction can be summarized as follows:
2 Ga(s) + 6 HCl(aq) → 2 GaCl₃(aq) + 3 H₂(g)
This reaction shows that 2 moles of gallium produce 3 moles of hydrogen gas.
First, we need to find the number of moles of gallium:
Molar mass of Ga = 69.72 g/mol
Number of moles of Ga = mass of Ga / molar mass of Ga
Number of moles of Ga = 8.88 g / 69.72 g/mol = 0.127 moles of Ga
According to the reaction stoichiometry, we need to multiply the moles of Ga by 1.5 to get the moles of hydrogen because 2 moles of Ga produce 3 moles of H₂:
Number of moles of H₂ = 0.127 moles Ga x (3 moles H₂ / 2 moles Ga) = 0.1905 moles H₂
Now, use the ideal gas law to find the volume:
PV = nRT
Where P = pressure, V = volume, n = number of moles, R = ideal gas constant, T = temperature in Kelvin (K)
Convert temperature to Kelvin:
T = 300.0 K (already given)
Convert pressure to atm (1 atm = 760 torr):
P = 723 torr x (1 atm / 760 torr) = 0.9513 atm
Use the ideal gas constant R = 0.0821 L·atm/(mol·K)
Solving for V:
V = nRT / P = (0.1905 moles H₂) x (0.0821 L·atm/(mol·K)) x (300.0 K) / (0.9513 atm) = 4.87 L
So, the volume of hydrogen gas produced under these conditions is approximately 4.87 L.