What mass of zinc would need to react with hydrochloric acid in order to produce 25.0 mL of hydrogen gas collected over water at 25 degrees celsius and 105 kPa.
How do you solve this using the combined gas laws?
The answer is 0.067 grams but how do you get there?
1) From a Table of Water Vapour Pressure (in kPa), find for water at 25 C, pressure = 3.17 kPa.
105.3 kPa - 3.17 kPa = 101.83 kPa
2) gas law constant, R = 0.0821 L-atm/mol-K
Convert other units to match those used in R:
101.83 kPa/101.325 kPa/atm = 1.005 atm
25 mL = 0.025 L
25 C + 273.15 = 298.15 K
Moles of H2:
Using PV = nRT, substitute the above and solve for n to get 0.001026 mol H2.
Now balance the chemical equation:
Zn + 2HCl --> H2 + ZnCl2
Ratio of Zn to H2 is 1:1, therefore,
0.001026 mol H2 x 1 mol Zn/1mol H2
=0.001026 mol Zn
0.001026 mol Zn x 65.38 g/mol Zn
= 0.067 g Zn
I know how to solve it using the ideal gas law, but how do you solve it using the combined gas laws?
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Gas Law Problems- Combined Gas Law
Chemteam comes up first - worksheet with solutions to some similar problems
To solve this problem using the combined gas laws, we need to consider the ideal gas law and Dalton's law of partial pressures.
Step 1: Convert the given volume of hydrogen gas collected over water (25.0 mL) to the volume of hydrogen gas at standard temperature and pressure (STP). This is necessary because the ideal gas law is typically used at STP conditions.
To do this, we can use the following equation:
V2 = V1 * (P1/P2) * (T2/T1)
Where:
- V1 is the initial volume (25.0 mL)
- P1 is the initial pressure (105 kPa)
- P2 is the standard pressure at STP (101.3 kPa)
- T1 is the initial temperature in Kelvin (25 + 273 = 298 K)
- T2 is the standard temperature at STP in Kelvin (273 K)
Plugging in the values, we get:
V2 = 25.0 mL * (105 kPa / 101.3 kPa) * (273 K / 298 K)
V2 ≈ 23.74 mL
Step 2: Apply Dalton's law of partial pressures to determine the pressure of the hydrogen gas alone. Since the hydrogen gas is collected over water, the total pressure is the sum of the pressure of hydrogen gas and the vapor pressure of water.
The vapor pressure of water at 25 degrees Celsius is approximately 3.17 kPa. Therefore, the pressure of the hydrogen gas alone is:
P_hydrogen = Total pressure - Vapor pressure of water
P_hydrogen = 105 kPa - 3.17 kPa
P_hydrogen ≈ 101.83 kPa
Step 3: Use the ideal gas law to relate the amount of hydrogen gas to the amount of reactant consumed.
The ideal gas law equation is:
PV = nRT
Where:
- P is the pressure of the gas (in this case, hydrogen gas alone, 101.83 kPa)
- V is the volume of gas at STP (23.74 mL, converted to liters by dividing by 1000)
- n is the number of moles of gas (unknown - we'll solve for this)
- R is the ideal gas constant (8.314 L·kPa·K⁻¹·mol⁻¹)
- T is the temperature (273 K, standard temperature at STP)
Rearranging the ideal gas law equation to solve for n, we get:
n = (PV) / (RT)
Plugging in the values, we have:
n = (101.83 kPa * 0.02374 L) / (8.314 L·kPa·K⁻¹·mol⁻¹ * 273 K)
n ≈ 0.00119 mol
Step 4: Calculate the molar mass of zinc (Zn) using the periodic table. The molar mass of zinc is 65.38 g/mol.
Step 5: Use the molar ratio from the balanced chemical equation to convert moles of zinc to mass of zinc.
The balanced chemical equation for the reaction between zinc and hydrochloric acid is:
Zn + 2HCl → ZnCl₂ + H₂
From the equation, we see that 1 mole of zinc (Zn) reacts to produce 1 mole of hydrogen gas (H₂).
Therefore, the mass of zinc needed is:
mass_zinc = n * molar_mass_zinc
mass_zinc = 0.00119 mol * 65.38 g/mol
mass_zinc ≈ 0.07763 g
The answer rounded to three significant figures is approximately 0.078 g (not 0.067 g as previously stated).