Question

How much copper is present in \(50 \mathrm{~g}\) of \(\mathrm{CuSO}_{4} ?\) (a) \(19.90 \mathrm{~g}\) (b) \(39.81 \mathrm{~g}\) (c) \(63.5 \mathrm{~g}\) (d) \(31.71 \mathrm{~g}\)

Short answer

The mass of copper in a 50 g sample of CuSO4 is 19.90 g.

Step-by-step solution

Calculate the molar mass of CuSO4

Determine the molar mass of copper(II) sulfate (CuSO4) by adding the atomic masses of the individual elements. The atomic masses (rounded to the nearest tenth) are approximately 63.5 g/mol for copper (Cu), 32.1 g/mol for sulfur (S), and 16.0 g/mol for each oxygen (O) atom. The formula for molar mass is: Molar Mass of CuSO4 = Atomic Mass of Cu + Atomic Mass of S + 4 × Atomic Mass of O.

Calculate the mass percentage of copper in CuSO4

Find the mass percentage of copper in CuSO4 by taking the atomic mass of copper and dividing it by the molar mass of CuSO4, then multiply by 100 to get the percentage: Mass Percentage of Cu = (Atomic Mass of Cu / Molar Mass of CuSO4) × 100%.

Calculate the mass of copper in the given sample

Use the mass percentage of copper in CuSO4 to determine the mass of copper present in a 50 g sample of CuSO4: Mass of Cu = Mass Percentage of Cu × Total Mass of CuSO4 Sample / 100.

Key concepts

Molar Mass

Understanding the molar mass of a substance is crucial in chemistry. It is the mass of one mole of a given substance, expressed in grams per mole (g/mol). This concept is vital because it relates the mass of substances to the number of particles contained, namely atoms or molecules. To calculate the molar mass, you sum up the atomic masses of each element within a compound multiplied by their respective numbers in the molecular formula.

As seen in the exercise, to find the molar mass of copper(II) sulfate (CuSO₄), you first identify each element's atomic mass. Then, multiply each atomic mass by the number of atoms in the formula and add everything together. This step is fundamental as it sets the groundwork for most stoichiometric calculations in chemistry.

Mass Percentage

The mass percentage, also known as mass percent composition, is a measure of concentration that expresses the mass of a particular component (in this case, copper) as a percentage of the total mass of the compound. To find the mass percentage of copper in copper(II) sulfate, divide the atomic mass of copper by the molar mass of CuSO₄ and multiply the result by 100%. This calculation tells you what fraction of the total mass is due to copper. This figure is useful for understanding the composition of compounds and is essential when you need to know how much of a specific element is present in a substance.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and the products in a chemical reaction. It involves using the coefficients of a balanced chemical equation to calculate the relative amounts of reactants and products. In the context of the exercise, stoichiometry enables us to determine the mass of copper present in a given quantity of copper(II) sulfate based on the proportional relationship dictated by its chemical formula. By using the mass percentage previously calculated, stoichiometry allows us to find out exactly how much copper can be obtained from a 50 g sample of CuSO₄.

Atomic Mass

The atomic mass of an element, often listed in the periodic table, is the weighted average mass of the atoms in a naturally occurring sample of the element. It takes into account the various isotopes of the element and their abundance. This value, normally expressed in atomic mass units (u) or grams per mole (g/mol), is critical for calculating both the molar mass of compounds and mass percentages. For example, the atomic mass of copper is approximately 63.5 g/mol, which directly influences the calculation of the molar mass of compounds containing copper, such as CuSO₄.

Molecular Formula

The molecular formula provides the actual number of atoms of each element in a molecule of a compound. For instance, CuSO₄ indicates that each molecule is composed of one copper atom, one sulfur atom, and four oxygen atoms. The molecular formula is crucial when determining the molar mass because it allows you to add up the atomic masses of the elements in their specific ratios. It is also used in stoichiometric calculations to correlate the mass of a compound to the amount of an element it contains, such as the quantity of copper in copper(II) sulfate, summarizing the whole concept into one succinct representation of the compound's composition.