Question

A compound of \(\mathrm{Ca}, \mathrm{C}, \mathrm{N},\) and \(\mathrm{S}\) was subjected to quantitative analysis and formula mass determination, and the following data were obtained. A \(0.250 \mathrm{~g}\) sample was mixed with \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) to convert all of the Ca to \(0.160 \mathrm{~g}\) of \(\mathrm{CaCO}_{3}\). A \(0.115 \mathrm{~g}\) sample of the compound was carried through a series of reactions until all of its \(S\) was changed to \(0.344 \mathrm{~g}\) of \(\mathrm{BaSO}_{4}\). A \(0.712 \mathrm{~g}\) sample was processed to liberate all of its \(\mathrm{N}\) as \(\mathrm{NH}_{3}\), and \(0.155 \mathrm{~g}\) of \(\mathrm{NH}_{3}\) was obtained. The formula mass was found to be 156 . Determine the empirical and molecular formulas of this compound.

Short answer

Calculate individual moles of Ca, N, and S; determine the mass of C; find empirical formula by mole ratio; multiply subscripts by the formula mass / empirical formula mass ratio to get the molecular formula.

Step-by-step solution

Determine moles of Ca in CaCO3

To find the moles of Ca in CaCO3, use the mass of CaCO3 and its molar mass. The molar mass of CaCO3 (Ca=40, C=12, O=3x16=48) is 100 g/mol. Calculate moles of CaCO3 from 0.160 g by the equation: moles = mass (g) / molar mass (g/mol).

Calculate moles of N in NH3

Find the moles of nitrogen in NH3 using its mass (0.155 g) and the molar mass of NH3 (N=14, H=3x1=3, total=17 g/mol). Calculate moles of N using the mass of NH3 as follows: moles = mass (g) / molar mass (g/mol).

Determine moles of S in BaSO4

To determine the moles of sulfur, use the mass of BaSO4 (0.344 g) and its molar mass (Ba=137, S=32, O=4x16=64; total=233 g/mol). Convert the mass of BaSO4 to moles of S through the equation: moles = mass (g) / molar mass (g/mol).

Find moles of Ca, N, and S in the original samples

For Ca: Divide the moles obtained in Step 1 by the mass of the original sample (0.250 g). For N: Divide the moles obtained in Step 2 by the mass of the original sample (0.712 g). For S: Divide the moles obtained in Step 3 by the mass of the original sample (0.115 g).

Calculate the mass of C in the compound

Assuming 100 g of the compound, use the mass percentage of Ca, S, and N to find the mass of C. Subtract the mass of Ca, S, and N from 100 g to get the mass of C. Calculate moles of C using its atomic mass.

Determine mole ratios to get the empirical formula

Using the moles of Ca, S, N, and C, find the simplest whole number ratio by dividing all moles by the smallest value among them. This ratio gives the subscripts for the atoms in the empirical formula.

Calculate the empirical formula mass

Add the atomic masses of the atoms in the empirical formula according to the subscripts obtained in Step 6 to find the empirical formula mass.

Determine the molecular formula

Divide the given formula mass (156) by the empirical formula mass obtained in Step 7 to find the multiple. Multiply all subscripts in the empirical formula by this multiple to get the molecular formula.

Key concepts

Quantitative Chemical Analysis

Quantitative chemical analysis is a critical process in chemistry that involves determining the exact mass or concentration of elements and compounds in a sample. This type of analysis is essential for identifying the composition or purity of a substance. For instance, in the exercise provided, quantitative analysis techniques have been utilized to determine the amounts of calcium (Ca), sulfur (S), and nitrogen (N) in a given compound.

By converting elements to specific compounds such as Ca to CaCO3, S to BaSO4, and N to NH3, and subsequently measuring their masses, we can calculate the moles of each element present in the original sample. This step is fundamental, as the amount of substance measured in moles reflects the number of atoms or molecules, providing a basis for stoichiometric calculations and further analyses to determine empirical and molecular formulas.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships, or ratios, of reactants and products in chemical reactions. In the context of the exercise, stoichiometry involves using the moles of each element determined from quantitative analysis to establish the ratios between them in the compound.

By comparing the number of moles of each element, we can derive a mole ratio and simplify this to whole numbers to ascertain the empirical formula. For a clear understanding, imagine stoichiometry as a recipe that outlines the proportions of ingredients needed to create a certain dish. The precise mole ratios are critical as they ultimately guide us in determining the compound's simplest formula and, with subsequent calculations, the molecular formula.

Molar Mass Calculation

The molar mass calculation is fundamental for converting between the mass of a substance and the number of moles. Since a mole is defined based on the number of atoms in 12 grams of carbon-12, the molar mass is the weight in grams of one mole of a substance, which matches the substance's atomic or molecular weight expressed in atomic mass units (amu).

In our exercise, the molar mass of each compound (CaCO3, BaSO4, and NH3) created from elements in the original sample allowed us to calculate the moles of the respective elements by using the formula: \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\). It is essential to grasp how molar mass acts as the bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe.

Chemical Compound Composition

The composition of a chemical compound involves understanding what elements are present and in what proportions. This is deduced by determining the empirical formula, which gives the simplest whole-number ratio of atoms in the compound, and the molecular formula, which shows the actual number of atoms of each element in a molecule of the compound.

The weights obtained from quantitative chemical analysis are converted to moles, which are then used to calculate the empirical formula. Improving your understanding of chemical compound composition involves practice in converting mass to moles, recognizing stoichiometric relationships among elements, and refining techniques to deduce empirical and molecular formulas. The analysis that leads us from individual element masses in a compound to the discovery of its overall formula showcases the beauty and precision of chemical science.