Question

A sample of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) contains \(2.02 \mathrm{g}\) of hydrogen, \(32.07 \mathrm{g}\) of sulfur, and \(64.00 \mathrm{g}\) of oxygen. How many grams of sulfur and grams of oxygen are present in a second sample of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) containing 7.27 g of hydrogen?

Short answer

In the second sample containing 7.27 g of hydrogen, there are 115.47 g of sulfur and 230.31 g of oxygen present.

Step-by-step solution

Calculate Molar Mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\)

First, we need to calculate the molar mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\). To do this, sum up the molar mass of each element in the compound. The molar mass of hydrogen (H) = 1 g/mol The molar mass of sulfur (S) = 32 g/mol The molar mass of oxygen (O) = 16 g/mol Molar mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) = (2 × 1) + 32 + (4 × 16) = 98 g/mol

Mass ratios for the first sample

The given masses of elements in the first sample are: Hydrogen = 2.02 g Sulfur = 32.07 g Oxygen = 64.00 g We need the mass ratios of sulfur (S) and oxygen (O) to hydrogen (H) in the first sample. Mass ratio of S:H = (mass of S) / (mass of H) = 32.07 / 2.02 = 15.87 Mass ratio of O:H = (mass of O) / (mass of H) = 64.00 / 2.02 = 31.68

Calculate the mass of S and O in the second sample

In the second sample, we know the mass of hydrogen (H) = 7.27 g. Now, we use the mass ratios calculated for the first sample to find the mass of S and O in the second sample: Mass of sulfur (S) in the second sample = mass ratio of S:H × mass of H in the second sample Mass of sulfur (S) in the second sample = 15.87 × 7.27 = 115.47 g Mass of oxygen (O) in the second sample = mass ratio of O:H × mass of H in the second sample Mass of oxygen (O) in the second sample = 31.68 × 7.27 = 230.31 g The sulfur and oxygen present in the second sample are 115.47 g and 230.31 g respectively.

Key concepts

Molar Mass Calculation

Molar mass calculation is an essential step in stoichiometry, a branch of chemistry that focuses on the quantitative relationships between the reactants and products in a chemical reaction. Understanding molar mass is vital when dealing with chemical equations and helps in the measurement of chemical substances involved.

To calculate the molar mass, one must know the atomic masses of each element involved in a compound. These atomic masses are usually expressed in grams per mole (g/mol), representing the mass of one mole of atoms of an element. The atomic masses are then multiplied by the number of atoms of each element present in the compound and added together to give the molar mass of the compound. For instance:

• Molar mass of hydrogen (H) = 1 g/mol
• Molar mass of sulfur (S) = 32 g/mol
• Molar mass of oxygen (O) = 16 g/mol

To obtain the molar mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), you would calculate it as follows:\[\text{Molar mass of } \mathrm{H}_{2} \mathrm{SO}_{4} = (2 \times 1) + 32 + (4 \times 16) = 98 \text{ g/mol}\].

This molar mass is then used as a conversion factor between the amount of substance in moles and its mass in grams, making it a fundamental concept in chemical composition analysis.

Chemical Composition

Chemical composition refers to the identification and proportion of the elements that constitute a chemical compound. Understanding the chemical composition is critical for predicting the compound's properties, behavior, and reactivity. Each compound has a unique formula that represents the actual number of atoms of each element present in the compound.

For sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), the chemical composition can be defined by the molecular formula where two hydrogen atoms, one sulfur atom, and four oxygen atoms are bonded together. By knowing the molar mass of the compound and the chemical composition, one can determine the percentage composition of each element. This information is utilized to deduce how different elements contribute to the overall mass of the compound in any given sample.

Since we know that sulfuric acid has a consistent composition, if we have the mass of one element from a sample, we can calculate the masses of the other elements in any sample of sulfuric acid, as shown in the original problem.

Mass Ratio

The mass ratio plays a pivotal role in stoichiometry to compare the mass of different elements within a compound or different compounds involved in a reaction. It serves as a bridge to relate the masses of elements when dealing with various samples of the same compound.

In the case of sulfuric acid, \(\mathrm{H}_{2} \mathrm{SO}_{4}\), we establish the mass ratio by observing the relationship between each element's mass to a chosen reference element, typically hydrogen due to its simple molar mass of 1 g/mol. For example, the mass ratio of sulfur to hydrogen (S:H) in a given sample can be calculated as the mass of sulfur divided by the mass of hydrogen. Similarly, the mass ratio of oxygen to hydrogen (O:H) is calculated by dividing the mass of oxygen by the mass of hydrogen:

• Mass ratio of S:H = \(\frac{\text{mass of S}}{\text{mass of H}}\)
• Mass ratio of O:H = \(\frac{\text{mass of O}}{\text{mass of H}}\)

These ratios remain consistent across different samples of the same compound, allowing us to use them to calculate the unknown masses of elements in other samples, as long as we have one known mass to work from. This principle is extensively applied in quantitative analysis in chemistry.