Problem 60 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

A sample of pure Cu \((4.00 \mathrm{~g})\) heated in a stream of oxygen for some time, gains in weight with the formation of black oxide of copper \((\mathrm{CuO})\). The final mass is 4.90 g. What per cent of copper remains unoxidized? \((\mathrm{Cu}=64)\) (a) \(90 \%\) (b) \(10 \%\) (c) \(20 \%\) (d) \(80 \%\)

Step-by-Step Solution

Answer

80% of copper remains unoxidized.

Step 1: Determine the mass of CuO formed

Subtract the initial mass of the copper from the final mass to determine the mass of copper oxide (CuO) that was formed: 4.90 g (final mass) - 4.00 g (initial mass of pure Cu) = 0.90 g (mass of CuO formed).

Step 2: Calculate the moles of Cu in CuO

Use the molar mass of Cu (64 g/mol) to calculate the moles of Cu that reacted to form CuO. Since the formula for copper oxide is CuO, each mole of CuO contains one mole of Cu.Number of moles of Cu in CuO = Mass of CuO formed / Molar mass of Cu = 0.90 g / 64 g/mol = 0.0140625 moles.

Step 3: Calculate the mass of Cu that reacted

Multiply the number of moles of Cu that reacted by the molar mass of Cu to get the mass:Mass of Cu reacted = Moles of Cu * Molar mass of Cu = 0.0140625 moles * 64 g/mol = 0.899 g.

Step 4: Calculate the mass of unreacted Cu

Subtract the mass of Cu that reacted from the initial mass of Cu to find the mass of unreacted Cu:4.00 g (initial Cu) - 0.899 g (reacted Cu) = 3.101 g (unreacted Cu).

Step 5: Calculate the percentage of unreacted Cu

The percentage of unreacted copper is the mass of unreacted Cu divided by the initial mass of Cu, multiplied by 100:Percentage of unreacted Cu = (Mass of unreacted Cu / Initial mass of Cu) * 100 = (3.101 g / 4.00 g) * 100 = 77.525%.

Step 6: Round to significant figures

Since the initial mass of Cu was given to two decimal places, the percentage should also be rounded to two decimal places:77.525% rounds to 77.53% which is nearest to 80%. Hence, the answer is option (d) 80%.

Key Concepts

Chemical Stoichiometry

Chemical stoichiometry is the ballpark of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. In the given problem, stoichiometry plays a crucial role in determining the extent of copper's reaction with oxygen to form copper(II) oxide (CuO).

Using stoichiometry, one can infer the mole-to-mole ratios from the balanced chemical equation for the formation of CuO from Cu and O₂, which is typically a 1:1 relationship since one mole of copper reacts with half a mole of oxygen to produce one mole of copper(II) oxide. Though the equation isn't explicitly provided here, this mole ratio is used implicitly to determine the amount of copper that has reacted. In this case, stoichiometry allows us to understand that the theoretical yield of CuO is directly tied to the initial amount of copper, subject to the limiting reactant, which in this scenario is copper itself.

Molar Mass Calculation

Understanding the molar mass calculation is paramount for solving problems involving chemical stoichiometry. Molar mass, defined as the mass of one mole of a substance, serves as a conversion factor between the mass of a substance and the amount of substance in moles.

For example, in the provided exercise, the molar mass of Cu is given as 64 g/mol. This means every mole of copper weighs 64 grams. Having this information enables us to calculate how many moles of copper reacted by dividing the mass of CuO formed, found in step 1, by the molar mass of copper. It's vital to note that even though CuO is formed, the stoichiometric calculations rely solely on the molar mass of Cu because CuO contains one atom of copper per molecule, hence the molar mass of copper is all that's needed for these calculations.

Percent Composition

Percent composition is a measure of the relative amounts of elements within a compound or a mixture. It represents the mass percentage of each element in the substance. Solving for percent composition requires finding the mass of the element or components of interest and dividing by the total mass, then multiplying the result by 100 to get a percentage.

In the context of the exercise provided, we are asked to find what percent of copper remains unoxidized after the reaction. After calculating the mass of the unreacted copper, we compare this to the original mass. It's crucial to remember to maintain consistent units and significant figures as seen in Step 5 and 6 of the solution process. This concept not only gives us the percentage of the element in a compound but also helps in understanding the extent to which a reaction has proceeded, based on the unreacted starting material.