Question

In the electrolysis of a CuSO \(_{4}\) solution, how many grams of Cu are plated out on the cathode in the time that it takes to liberate \(5.6\) litre of \(\mathrm{O}_{2}(\mathrm{~g})\), measured at \(\mathrm{STP}\), at the anode? (a) \(31.75\) (b) \(14.2\) (c) \(4.32\) (d) None of these

Short answer

31.75 grams of Cu are plated out on the cathode.

Step-by-step solution

Determine moles of oxygen gas

At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 liters. Calculate the moles of oxygen gas liberated using the formula: number of moles = volume of gas at STP / molar volume at STP.

Determine moles of copper

The electrolysis of copper(II) sulfate involves the following half-reaction at the anode: 2H2O(l) → O2(g) + 4H+(aq) + 4e-. Four moles of electrons are needed to produce one mole of oxygen. Since copper plates out at the cathode in a one-to-one ratio with the electrons (Cu2+ + 2e- → Cu), for every 1 mole of O2, 4 moles of Cu will plate out. Multiply the moles of oxygen by 4 to find the moles of copper.

Calculate mass of copper plated

Find the mass of copper by using the molar mass of copper which is approximately 63.5 g/mol. Use the formula: mass = moles * molar mass. Calculate the mass of copper that corresponds to the number of moles obtained in Step 2.

Key concepts

Molar Volume at STP

The molar volume of a gas is the volume occupied by one mole of the gas under certain conditions of temperature and pressure. At STP, which stands for Standard Temperature and Pressure (0°C and 1 atm), one mole of any gas occupies a volume of 22.4 liters. This uniformity makes calculations involving gases quite convenient.

For instance, if you're asked how many moles of gas are present in a given volume at STP, you can simply divide the given volume by 22.4 liters. So, if you have 5.6 liters of oxygen gas at STP, you calculate the moles of oxygen as follows: \[\text{moles of oxygen} = \frac{5.6 \text{ liters}}{22.4 \text{ liters/mole}}\].

This concept is critical in the electrolysis of copper sulfate, as it allows us to find the amount of copper that will be deposited based on the volume of oxygen gas liberated at the anode.

Half-Reaction in Electrolysis

Electrolysis is the process of causing a chemical reaction to occur by passing an electric current through a substance. In the case of copper sulfate electrolysis, the reactions at the electrodes can be split into half-reactions. The half-reaction at the cathode typically involves reduction, where copper ions gain electrons to form copper metal.

At the anode, the half-reaction for the electrolysis of water is: \[2\text{H}_2\text{O(l)} \rightarrow \text{O}_2\text{(g)} + 4\text{H}^+\text{(aq)} + 4e^-\].

This indicates that for every molecule of oxygen gas produced (O₂), four electrons are released. Understanding the stoichiometry of this half-reaction is essential to determine the relationship between the oxygen gas produced and the amount of copper that will be deposited at the cathode.

Calculation of Moles

The calculation of moles forms the crux of many stoichiometric problems in chemistry. A mole is essentially a unit of measurement used to express amounts of a chemical substance. It is defined as the amount of any substance that contains the same number of elementary entities as there are atoms in 12 grams of pure carbon-12.

In the context of our problem, once we've established the volume of oxygen at STP, we can calculate the moles of oxygen using the molar volume of a gas at STP. Knowing the moles of oxygen and the stoichiometry of the electrolysis reaction allows us to determine the moles of copper that will be deposited: since 1 mole of O₂ corresponds to 4 moles of Cu, we can simply multiply the moles of oxygen by four to get the moles of copper.

Molar Mass

Molar mass is another pivotal concept in chemistry, which is the mass of one mole of a substance expressed in grams per mole (g/mol). It can be found by summing the atomic masses of all the atoms in a molecule as provided by the periodic table.

In our exercise, the molar mass of copper is used to convert moles into grams to find out how much copper is deposited during electrolysis. The molar mass of copper (Cu) is 63.5 g/mol. To find the mass of copper deposited, you would use the formula: \[\text{mass of Cu} = \text{moles of Cu} \times \text{molar mass of Cu (63.5 g/mol)}\].

By applying this formula, we can calculate the exact mass of copper that is plated out at the cathode during the given electrolysis scenario.