Final answer:
To find the mass of magnesium needed to produce a specific volume of hydrogen gas, calculate the number of moles of hydrogen using the ideal gas law and stoichiometry,
Step-by-step explanation:
To calculate the mass of magnesium (Mg) needed to produce 29.0 ml of hydrogen gas (H₂) at an atmospheric pressure of 739 mmHg and a temperature of 25.9°C, we must first use the ideal gas law PV = nRT to find the number of moles of hydrogen gas.
The ideal gas constant (R) will be used in its value of 0.08206 (L•atm)/(K•mol), so we will need to convert the temperature to Kelvin (T = 25.9 + 273 = 298.9 K) and the pressure from mmHg to atm (739 mmHg = 739/760 atm).
Once we have determined the number of moles of hydrogen, we can use stoichiometry to find the moles of magnesium needed, since the ratio is 1:1 according to the balanced chemical equation.
From there, we multiply the number of moles of Mg by its molar mass, 24.305 g/mol, to find the mass in grams.