Problem 19 - Chemistry Matter and Change

Question

A 78.0-g sample of an unknown compound contains 12.4 g of hydrogen. What is the percent by mass of hydrogen in the compound?

Step-by-Step Solution

Answer

The percent by mass of hydrogen in the unknown compound is approximately 15.89%.

Step 1: Identify the given information

We are given: - Mass of the unknown compound: 78.0 g - Mass of hydrogen in the compound: 12.4 g

Step 2: Apply the percent by mass formula

Percent by mass = (mass of component / total mass) × 100 In our case, the component is hydrogen, and we can plug the given values into the formula: Percent by mass of hydrogen = (mass of hydrogen / total mass of the compound) × 100

Step 3: Insert given values and calculate the percent by mass

Percent by mass of hydrogen = (12.4 g / 78.0 g) × 100 Now, divide 12.4 by 78.0: Percent by mass of hydrogen = 0.1589... × 100 Finally, multiply by 100 to get the percentage: Percent by mass of hydrogen = 15.89 % The percent by mass of hydrogen in the unknown compound is approximately 15.89%.

Key Concepts

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the calculation of the quantities of substances involved in chemical reactions. It is founded on the law of conservation of mass and the relationships we can derive from balanced chemical equations, often referred to as stoichiometric coefficients. These calculations are crucial for scientists to produce the desired amount of products without wasting reactants.

To start with stoichiometry, one should understand the concept of the mole, which is the standard unit for amount of substance in chemistry. It allows chemists to count particles by weighing, as one mole corresponds to Avogadro's number, approximately 6.022 x 10^23 particles. Stoichiometry is intertwined with the percent by mass concept when determining the composition of a compound or the necessities for a reaction. For instance, in our exercise, the stoichiometry concept is used to deduce the percent composition (by mass) of hydrogen in a sample, which is the initial step often required to further identify the compound or to use this compound in a stoichiometric calculation for a reaction.

Chemical Composition

Chemical composition refers to the identification and proportion of the elements within a chemical substance. The knowledge of chemical composition is key for determining the properties of a compound and how it will behave in chemical reactions.

When we talk about a compound's percentage by mass, we're focusing on the mass ratio of each element contained in a compound to the entire mass of the compound, expressed as a percentage. This is a vital measure in chemistry since it allows us to understand the makeup of a substance and relate this to its chemical formula. For example, in our exercise, knowing that hydrogen makes up approximately 15.89% of the compound by mass can help deduce the compound's empirical formula, thereby unveiling more detailed information about its chemical composition. Understanding this will facilitate predictions about reactivity and interaction with other compounds, as well as adapting the right methodologies when handling the substance in practical applications.

Chemical Formula Calculation

Chemical formula calculation is the process of deducing the empirical or molecular formula of a compound from its compositional data. The empirical formula represents the simplest whole-number ratio of atoms of each element in a compound, while the molecular formula is the exact number of atoms of each element in a molecule of the compound.

Using the percent by mass found in the exercise, we could potentially determine the empirical formula of the compound if we had the percent by mass of the other elements present. Once you divide the mass percentage of each element by its atomic mass, you can simplify the resulting ratios to the smallest whole numbers, which gives you the empirical formula. If additional data is provided, such as the molar mass of the compound, we can find out the molecular formula as well, which is a crucial step in understanding the quantitative aspects of chemical reactions. These formulas are essential for stoichiometry calculations, which in turn can reveal a lot about the substance's reactivity, potential use in different industries, and its role in various chemical processes.