Question

Calcium carbide, \(\mathrm{CaC}_{2},\) was once used to make signal flares for ships. Water dripped onto \(\mathrm{CaC}_{2}\) reacts to give acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\), which burns brightly. One sample of \(\mathrm{CaC}_{2}\) contains \(0.150 \mathrm{~mol}\) of carbon. How many moles and how many grams of calcium are also in the sample?

Short answer

The sample contains 0.075 moles and 3.006 grams of calcium.

Step-by-step solution

Determine the Mole Ratio

Start by writing the chemical formula for calcium carbide: \(\mathrm{CaC}_{2}\). The formula indicates that in each molecule of calcium carbide, there is one calcium atom for every two carbon atoms. Since the sample contains 0.150 mol of carbon, we can determine the moles of calcium based on this ratio: for every 2 moles of carbon, there is 1 mole of calcium.

Calculate the Moles of Calcium

As established in step 1, the mole ratio between calcium and carbon in calcium carbide is 1:2. Thus, we divide the given moles of carbon by 2 to find the moles of calcium: \(\frac{0.150 \text{ mol C}}{2} = 0.075 \text{ mol Ca}\).

Calculate the Mass of Calcium in Grams

To convert moles of calcium to grams, we use the molar mass of calcium, which is approximately 40.08 g/mol. The mass of calcium in grams is calculated by multiplying the moles by the molar mass: \(0.075 \text{ mol Ca} \times 40.08 \text{ g/mol} = 3.006 \text{ g Ca}\).

Key concepts

Chemical Reactions

Understanding chemical reactions is essential in chemistry as they describe how substances change into new materials. A chemical reaction involves the breaking of bonds in the reactants and the formation of new bonds in the products. In the instance of calcium carbide reacting with water to produce acetylene, which is used in signal flares, we're looking at a type of chemical reaction where a solid interacts with a liquid to produce a gas.

In such reactions, it’s crucial to balance the equation to adhere to the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a closed system. By analyzing the equation for our specific scenario, we determine the stoichiometry—the quantitative relationship between reactants and products in a chemical reaction. Thus, the stochiometric calculations guide us to find out that one mole of calcium in the compound will react to give us one mole of acetylene gas, illustrating the clear 1:1 relationship in this chemical transformation.

Molar Mass Calculation

Molar mass calculation is a key task in stoichiometry, serving as a bridge between the mass of a substance and the number of particles or moles present. The molar mass is defined as the mass of one mole of a substance and is measured in grams per mole (g/mol). It corresponds to the sum of the atomic masses of every atom present in the molecular formula of the substance.

To compute the molar mass, we refer to the periodic table where each element's atomic mass is given. For example, the molar mass of calcium (Ca) is about 40.08 g/mol. When tackling exercises such as the one involving calcium carbide, we use the molar mass to convert from moles to grams, facilitating the understanding of quantities involved in the real world, since we measure substances by mass, and this helps bridge the gap between microscopic (molecular) and macroscopic (bulk) levels of substances.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the microscopic world of atoms and molecules to the macroscopic world that we can measure. A mole is a unit that represents a very large quantity of entities, just as a dozen refers to twelve items. Avogadro's number, which is approximately 6.022 x 10^23, denotes the quantity of particles in one mole of substance, whether they are atoms, molecules, ions, or electrons.

In the context of the given exercise, understanding the mole concept allows us to manage the scale of chemical reactions. Knowing that the sample of calcium carbide contains 0.150 mol of carbon, we can use the mole concept to directly find out the corresponding moles of calcium in the compound. This is because the mole provides a direct proportion based on the chemical formula of the compound. Consequently, chemists and students alike use the mole concept to interpret and predict the outcomes of chemical reactions quantitatively.