A 0.0677 g sample of magnesium metal reacted with excess hydrochloric acid solution to produce
69.9 mL of hydrogen gas. The gas was collected over water at 21.0° C. The levels of water inside
and outside the gas collecting tube are identical (meaning that the pressure exerted by liquid
water in the gas measuring tube is 0). The vapor pressure of water at 21.0°C is 18.6 torr and the
atmospheric pressure is 755 torr. Calculate the experimental molar volume of hydrogen gas at
STP.
Reaction Equation _______________________________________________________________________
To calculate the experimental molar volume of hydrogen gas at STP, we first need to determine the number of moles of hydrogen gas generated in the reaction.
Step 1: Find the number of moles of magnesium (Mg)
Since we have the mass of magnesium and its molar mass, we can calculate the number of moles of magnesium.
The molar mass of magnesium (Mg) is 24.31 g/mol.
Given mass of magnesium (Mg) = 0.0677 g
Number of moles of magnesium (Mg) = mass / molar mass
Number of moles of magnesium (Mg) = 0.0677 g / 24.31 g/mol
Step 2: Write the balanced chemical equation for the reaction
The reaction between magnesium (Mg) and hydrochloric acid (HCl) produces hydrogen gas (H2) and magnesium chloride (MgCl2).
The balanced chemical equation is: Mg + 2HCl → MgCl2 + H2
Step 3: Determine the number of moles of hydrogen (H2)
From the balanced chemical equation, we can see that the mole ratio between magnesium and hydrogen is 1:1. This means that the number of moles of hydrogen gas formed is the same as the number of moles of magnesium used.
Number of moles of hydrogen (H2) = Number of moles of magnesium (Mg)
Step 4: Calculate the volume of hydrogen gas at 21.0°C and 755 torr
We know that the volume of hydrogen gas collected is 69.9 mL. However, we need to correct this volume to account for the vapor pressure of water at the given temperature.
Partial pressure of hydrogen gas (PH2) = Total pressure - Vapor pressure of water
Partial pressure of hydrogen gas (PH2) = 755 torr - 18.6 torr
Now we can use the ideal gas law to calculate the number of moles of hydrogen gas at 21.0°C and 755 torr.
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
However, the given pressure is in torr, so we need to convert it to atm.
1 atm = 760 torr
Partial pressure of hydrogen gas (PH2) = (755 torr - 18.6 torr) / 760 torr/atm
Now we can plug the values into the ideal gas law equation to calculate the number of moles of hydrogen gas.
(PH2)(V) = (n)(R)(T)
(Number of moles of hydrogen)(R)(21.0°C + 273.15) = (Partial pressure of hydrogen gas)(Volume)
Step 5: Calculate the number of moles of hydrogen gas at STP (Standard Temperature and Pressure)
STP conditions are defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm.
Using the equation:
(Number of moles of hydrogen gas at 21.0°C and 755 torr)(R)(21.0°C + 273.15 K) = (Partial pressure of hydrogen gas)(Volume at STP)
(Number of moles of hydrogen gas at 21.0°C and 755 torr) = (Partial pressure of hydrogen gas)(Volume at STP) / (R)(21.0°C + 273.15 K)
Step 6: Convert the number of moles of hydrogen gas at STP to molar volume
Molar volume is defined as the volume occupied by one mole of a substance at a specific temperature and pressure (STP conditions).
Molar volume of hydrogen gas at STP = Volume at STP (in liters) / Number of moles of hydrogen gas at STP
Now, you can input the values into the equation and calculate the experimental molar volume of hydrogen gas at STP.