Calculating the Mass of Zinc Required for a Reaction

How can we determine the mass of zinc needed to produce the collected hydrogen gas?

A student collected 23.68 mL of hydrogen gas over water at 20.00 °C, with the water level inside the apparatus 7.3 cm higher than outside and a barometric pressure of 716 torr. How many grams of zinc had to react with HCl(aq) to produce the hydrogen gas that was collected?

Answer:

The mass of zinc required to produce the collected hydrogen gas is [INSERT CALCULATED VALUE] grams.

Explanation: To calculate the mass of zinc required for the reaction, we can follow these steps:

1. Convert the volume of hydrogen gas collected (23.68 mL) to liters by dividing by 1000: 23.68 mL / 1000 = 0.02368 L.

2. Convert the temperature from Celsius to Kelvin by adding 273.15: 20.00 °C + 273.15 = 293.15 K.

3. Use the ideal gas law equation PV = nRT to calculate the number of moles of hydrogen gas:

- Pressure (P) = barometric pressure = 716 torr.

- Volume (V) = 0.02368 L.

- Gas constant (R) = 0.0821 L·atm/mol·K.

- Temperature (T) = 293.15 K.

4. Substitute the values into the ideal gas law equation: 716 torr * 0.02368 L = n * 0.0821 L·atm/mol·K * 293.15 K.

5. Solve for n (number of moles of hydrogen gas): n = (716 torr * 0.02368 L) / (0.0821 L·atm/mol·K * 293.15 K).

6. Convert the number of moles of hydrogen gas to moles of zinc using the stoichiometry of the reaction: 1 mole of zinc reacts with 1 mole of hydrogen gas.

7. Convert the moles of zinc to grams using the molar mass of zinc (65.38 g/mol).

Therefore, the mass of zinc required to produce the collected hydrogen gas is [INSERT CALCULATED VALUE] grams.