Question

A 100-g sample of an unknown salt contains 64 g of chlorine. What is the percent by mass of chlorine in the compound?

Short answer

The percent by mass of chlorine in the unknown salt can be calculated using the formula: Percent by mass = (Mass of chlorine / Total mass of sample) * 100%. Given a sample of 100 g with 64 g of chlorine, we plug in the given values: Percent by mass = (64 g / 100 g) * 100%. The percent by mass of chlorine in the compound is 64%.

Step-by-step solution

Identify the given values.

We are given the total mass of the sample (100 g) and the mass of chlorine in the sample (64 g).

Use the formula to find the percent by mass.

Now that we have the mass of chlorine and the total mass of the sample, we can use the formula to find the percent by mass: Percent by mass = (Mass of chlorine / Total mass of sample) * 100% Plug in the given values: Percent by mass = (64 g / 100 g) * 100%

Calculate the percent.

We now calculate the ratio of the mass of chlorine to the total mass and multiply by 100%: Percent by mass = (0.64) * 100%

Find the final answer.

Multiply 0.64 by 100% to get the percent by mass of chlorine in the compound: Percent by mass = 64% The percent by mass of chlorine in the unknown salt is 64%.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of the quantities of reactants and products involved in a chemical reaction. It's based on the balanced chemical equations and the principles of conservation of mass. Essentially, stoichiometry allows chemists to make predictions about the outcomes of reactions, such as how much product will form from a given amount of reactants.

Understanding stoichiometry is crucial when calculating the percent by mass, as it often requires a clear comprehension of the mole concept and how elements combine in fixed ratios according to their molar masses to form compounds. For instance, when calculating the percentage of chlorine in a salt, we're engaging in a stoichiometric calculation. We compare the mass of chlorine to the overall mass of the compound, utilizing stoichiometry as a tool to understand the composition of the compound.

Chemistry Problem Solving

Solving chemistry problems often requires a logical and step-by-step approach. In the case of finding a percent by mass, the steps start by clearly identifying the known values, which are, in this exercise, the total mass and the mass of a specific element in the compound. Having accurate data is just the starting point.

From there, applying the correct formula and performing the calculations is crucial. The usage of the percent by mass formula, \( \frac{\text{Mass of component}}{\text{Total mass of compound}} \times 100% \), is straightforward, but students must be careful to express all quantities in the correct units to ensure accuracy. By sticking to a methodical approach—one that is iterative and logical—students can solve a wide variety of problems in chemistry confidently and accurately.

Molar Mass

The molar mass of an element or compound is a fundamental concept in chemistry that represents the mass of one mole of that substance. It is expressed in units of grams per mole (g/mol). For elements, the molar mass is found on the periodic table and is approximately equal to the atomic mass of the element. For compounds, the molar mass is the sum of the molar masses of all the elements included in the formula, each multiplied by the number of atoms of that element in the formula.

Understanding molar mass is essential because it serves as a bridge between the mass of a substance and the number of moles of that substance, which is a central concept in stoichiometry. When calculating the percent by mass of chlorine in the sample, molar mass isn’t directly used, but it’s an underlying concept that more complex stoichiometric calculations often depend upon. For example, if we were to react the compound with other substances and needed to find out how much product could be produced, we would need to know the molar mass of the reactants involved.