Question

A 7.83 -g sample of HCN contains 0.290 g of \(\mathrm{H}\) and 4.06 \(\mathrm{g}\) of \(\mathrm{N}\) . Find the mass of carbon in a sample of HCN with a mass of 3.37 \(\mathrm{g}\) .

Short answer

The mass of carbon in a 3.37 g sample of HCN is 1.37 g.

Step-by-step solution

Calculate the mass of carbon in the original sample

Subtract the mass of hydrogen and nitrogen from the total mass of the HCN sample to find the mass of carbon. Use the equation: Mass of Carbon = Total mass - (Mass of Hydrogen + Mass of Nitrogen).

Determine the percentage composition of carbon

Calculate the percentage by mass of carbon in the sample by dividing the mass of carbon by the total mass of the original sample and then multiplying by 100. Use the equation: Percentage of Carbon = (Mass of Carbon / Total mass of HCN) * 100.

Calculate the mass of carbon in the new sample

Apply the percentage of carbon to the mass of the new sample to find the mass of carbon in the 3.37 g sample. Use the equation: Mass of Carbon in new sample = (Percentage of Carbon / 100) * Mass of new HCN sample.

Key concepts

Stoichiometry

Stoichiometry is the area of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's based on the conservation of mass where the total mass of the reactants equals the total mass of the products. The law of definite proportions states that a chemical compound always contains the same elements in the exact same proportions by mass.

For students to successfully solve stoichiometric problems, they need to be comfortable with converting between grams, moles, and molecules using the molar mass of substances. Also, understanding balanced chemical equations is crucial as they indicate the ratio in which reactants combine and products form. For instance, in the sample exercise, stoichiometry principles are used to determine the mass of carbon in a given sample of hydrogen cyanide (HCN) based on known masses of other elements.

Molecular Mass

Molecular mass, also known as molecular weight, is the sum of the atomic masses of all the atoms in a molecule. It's usually measured in atomic mass units (amu), where one amu is defined as one-twelfth the mass of a carbon-12 atom. To find the molecular mass of a compound, you would add up the atomic masses of each element in that compound given their respective number of atoms.

An understanding of molecular mass is fundamental for stoichiometry calculations. When determining the percentage composition or carrying out mole-to-gram conversions, the molecular mass is a required piece of information. For instance, the determination of the mass of carbon in the exercise involves recognizing that the molecular mass of HCN contributes to the proportional mass of carbon within the compound.

Percent Composition

The percent composition of a compound is a way of expressing the relative amount of each element within the compound. It's calculated by dividing the mass of each element by the total molecular mass of the compound and then multiplying by 100 to get a percentage. This calculation shows the contribution of each element to the overall mass of the molecule.

Understanding percent composition is critical when you want to recreate a compound based on its elemental makeup, or to confirm the identity of a compound by comparing calculated percentages with experimental data. In the textbook exercise, after finding the total mass of carbon in HCN, the next step is to calculate its percent composition. This value enables the calculation of the mass of carbon in any other sample of HCN, like the one weighing 3.37 g, by applying the same percentage.