Electrolysis of water produces hydrogen gas and oxygen gas, which can be collected over water:
2H2O(l) → 2H2(g) + O2(g)
An electrolysis reaction at 735 mmHg pressure produced 25.00L of gas at 25°C; at which
point, the vapor pressure of water is 23.76 torr. How many grams of water were electrolyzed to produce the mixture of gases?
To solve this problem, we need to use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Step 1: Convert the given pressures to the same units.
The pressure of the gas produced by electrolysis is given in mmHg, while the vapor pressure of water is given in torr. Since the ideal gas law equation requires pressure to be in the same units, we need to convert one of the pressures to match the other. Let's convert the vapor pressure of water to mmHg.
1 torr = 1 mmHg
Therefore, the vapor pressure of water in mmHg is 23.76 mmHg.
Step 2: Calculate the partial pressure of the gases produced.
The total pressure of the gas mixture is 735 mmHg, and the vapor pressure of water is 23.76 mmHg.
Therefore, the partial pressure of the gases produced is:
Partial pressure of hydrogen gas = Total pressure - Vapor pressure of water
= 735 mmHg - 23.76 mmHg
≈ 711.24 mmHg
Step 3: Convert the volume of the gas to moles.
Using the ideal gas law equation, we can rearrange it to solve for n (number of moles).
V = nRT / P
n = PV / RT
First, convert the volume of the gas to liters:
25.00 L
Now, convert the pressure to atm:
1 atm = 760 mmHg
Pressure in atm = 711.24 mmHg / 760 mmHg/atm
≈ 0.936 atm
Temperature must be in Kelvin. Convert from Celsius to Kelvin:
T(K) = T(C) + 273
T(K) = 25 + 273
T(K) = 298 K
Now we can calculate the number of moles:
n = (0.936 atm) * (25.00 L) / [(0.0821 L·atm/mol·K) * (298 K)]
n ≈ 1.025 mol
Step 4: Calculate the number of moles of water.
The balanced equation for the electrolysis of water tells us that 2 moles of water produce 2 moles of hydrogen gas. Therefore, the number of moles of water is equal to the number of moles of hydrogen gas.
Therefore, the number of moles of water electrolyzed is approximately 1.025 mol.
Step 5: Calculate the molar mass of water.
The molar mass of water (H2O) is approximately 18.015 g/mol.
Step 6: Calculate the mass of water electrolyzed.
Mass = Number of moles * Molar mass
Mass = 1.025 mol * 18.015 g/mol
Mass ≈ 18.47 g
Therefore, approximately 18.47 grams of water were electrolyzed to produce the mixture of gases.
To solve this problem, we need to determine the number of moles of gases produced and then convert it to grams using the molar mass of water (H2O). Here's how you can get the answer:
Step 1: Convert the pressure of the gases produced from mmHg to atm.
- The pressure of the gases produced is given as 735 mmHg.
- 1 atm = 760 mmHg, so to convert mmHg to atm, divide the pressure by 760.
735 mmHg ÷ 760 mmHg/atm = 0.9671 atm (rounded to four decimal places)
Step 2: Use the ideal gas law to calculate the number of moles of gases produced.
- The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.
- Rearrange the equation to solve for n: n = PV / RT
- P = pressure in atm
- V = volume in liters
- R = ideal gas constant = 0.0821 L.atm/(mol.K)
- T = temperature in Kelvin
Let's calculate the number of moles of gas produced:
n = (0.9671 atm) * (25.00 L) / (0.0821 L.atm/(mol.K) * (25 + 273) K
= 0.9671 * 25.00 / (0.0821 * 298)
= 0.9683 mol (rounded to four decimal places)
Step 3: Calculate the number of moles of water electrolyzed based on the balanced chemical equation.
- According to the balanced equation, for every 2 moles of H2O, we get 2 moles of H2 and 1 mole of O2.
- The ratio is 2 moles of H2O: 2 moles of H2: 1 mole of O2 = 1 mole of H2O: 1 mole of H2: 0.5 moles of O2
Since the balanced equation shows that 2 moles of H2O produce 2 moles of H2, the number of moles of H2O can be calculated as follows:
Moles of H2O = 0.9683 mol / 2 mol = 0.4842 mol (rounded to four decimal places)
Step 4: Convert moles of H2O to grams.
- To convert moles of H2O to grams, use the molar mass of water.
- The molar mass of H2O = 2(1.00794 g/mol) + 1(15.999 g/mol) = 18.015 g/mol
The mass of water can then be calculated as follows:
Mass of water = 0.4842 mol * 18.015 g/mol
= 8.72 g (rounded to two decimal places)
Therefore, approximately 8.72 grams of water were electrolyzed to produce the mixture of gases.