To calculate the experimental molar volume of hydrogen gas at STP, we need to gather some information and use the ideal gas law equation.
First, let's write the balanced chemical equation for the reaction. When magnesium reacts with hydrochloric acid, it produces magnesium chloride and hydrogen gas:
Mg + 2HCl → MgCl2 + H2
Now, the next step is to determine the moles of hydrogen gas produced in the reaction. To do this, we'll use the mass of the magnesium sample and the molar mass of magnesium.
The molar mass of magnesium (Mg) is approximately 24.31 g/mol. We have a sample of 0.0677 g of magnesium, so we can calculate the number of moles:
moles of Mg = mass of Mg / molar mass of Mg
moles of Mg = 0.0677 g / 24.31 g/mol
Next, we need to calculate the volume of hydrogen gas produced at 21.0 degrees Celsius. We have the volume of the gas collected over water, but we need to correct it for the vapor pressure of water.
First, let's calculate the partial pressure of hydrogen gas using the collected volume and the observed atmospheric pressure:
partial pressure of H2 = total pressure - vapor pressure of water
partial pressure of H2 = 755 mmHg - 18.6 mmHg
Now, let's convert the pressure to atm:
partial pressure of H2 = (755 mmHg - 18.6 mmHg) / 760 mmHg/atm
Next, we need to convert the collected volume of hydrogen gas to the volume at STP. According to the ideal gas law, the volume of a gas is directly proportional to the number of moles.
The equation for the ideal gas law is:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
At STP (Standard Temperature and Pressure), the pressure is 1 atm and the temperature is 273.15 K. So, we can use the following equation to calculate the volume of hydrogen gas at STP:
V(STP) = V(Collected) x (P(Collected) / P(STP)) x (T(STP) / T(Collected))
V(STP) = 69.9 ml x [(755 mmHg - 18.6 mmHg) / 760 mmHg/atm] x (273.15 K / (21.0 + 273.15) K)
Finally, to calculate the experimental molar volume of hydrogen gas at STP, we divide the volume (in liters) by the number of moles:
Experimental molar volume = V(STP) / moles of H2
Now, you can plug in the values and calculate the experimental molar volume of hydrogen gas at STP.