If I was designing an experiment where hydrogen gas was collected over a 0.1 M aqueous HCl solution from the reaction with zinc metal and I assume complete, rapid reaction, what mass of zinc would be used to collect between 50 and 100 mL of the gas?
Note: I calculated using the 100 mL or 0.1 L.
(Assume the atmospheric pressure is 1.00 atm and that the solution was at 25 C resulting in a water vapor pressure of 23.5 torr.)
My answer: 0.518 g
To calculate the mass of zinc needed to collect between 50 and 100 mL of hydrogen gas, we can use the ideal gas law and stoichiometry.
Step 1: Convert the given volume of hydrogen gas to moles
Since we are given the volume in mL, we need to convert it to liters:
50 mL = 0.05 L
100 mL = 0.1 L
Next, we need to convert the pressure from torr to atm by dividing by 760 (since 1 atm = 760 torr):
Water vapor pressure = 23.5 torr / 760 = 0.031 atm
To calculate the moles of hydrogen gas, we can use the ideal gas law:
PV = nRT
The pressure (P) is given as 1.00 atm, the volume (V) is either 0.05 L or 0.1 L (depending on if you want to calculate for 50 mL or 100 mL), and the temperature (T) is 25°C, which we need to convert to Kelvin by adding 273:
T = 25°C + 273 = 298 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n) of hydrogen gas:
n = PV / RT
Substituting the values, we get:
n = (1.00 atm - 0.031 atm) * (0.05 L or 0.1 L) / (0.0821 L·atm·K^−1·mol^−1 * 298 K)
Step 2: Determine the mole ratio between zinc and hydrogen gas
Based on the balanced equation, the stoichiometric ratio between zinc and hydrogen gas is 1:1. This means that 1 mole of zinc reacts to produce 1 mole of hydrogen gas.
Step 3: Calculate the mass of zinc
Since the mole ratio is 1:1 for zinc and hydrogen, the mass of zinc will be equal to the number of moles of hydrogen gas produced.
Finally, we can calculate the mass of zinc by multiplying the number of moles of hydrogen gas (derived in step 1) by the molar mass of zinc, which is 65.38 g/mol:
mass of zinc = moles of hydrogen * molar mass of zinc
Using this approach, you should get the mass of zinc required to collect between 50 and 100 mL of hydrogen gas. In this case, the answer would be 0.518 g.