Problem 61 - Chemistry Matter and Change

Question

Welding If 5.50 mol of calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with an excess of water, how many moles of acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right),\) a gas used in welding, will be produced? \begin{equation} \mathrm{CaC}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})+\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g}) \end{equation}

Step-by-Step Solution

Answer

5.50 moles of acetylene \( \mathrm{C}_{2} \mathrm{H}_{2} \) will be produced.

Step 1: Identify the Chemical Reaction

The chemical reaction given is \( \mathrm{CaC}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca(OH)}_{2} + \mathrm{C}_{2} \mathrm{H}_{2} \). This shows the reaction between calcium carbide and water to produce calcium hydroxide and acetylene.

Step 2: Determine Mole Ratios

From the balanced chemical equation, the coefficients indicate that 1 mole of \( \mathrm{CaC}_2 \) produces 1 mole of \( \mathrm{C}_2 \mathrm{H}_2 \). The mole ratio between calcium carbide and acetylene is therefore 1:1.

Step 3: Calculate Moles of Acetylene Produced

Since the mole ratio between \( \mathrm{CaC}_{2} \) and \( \mathrm{C}_{2} \mathrm{H}_{2} \) is 1:1, 5.50 moles of calcium carbide will produce 5.50 moles of acetylene when reacted with an excess of water.

Key Concepts

Mole Ratio

The concept of a mole ratio is central to stoichiometry, which is the part of chemistry that calculates the quantities of reactants and products involved in a chemical reaction. A mole ratio is derived from the coefficients of a balanced chemical equation. It tells us the proportions in which substances participate in the reaction.
For instance, in the reaction of calcium carbide (\[\mathrm{CaC}_{2}\]) with water, the balanced equation is:\[ \mathrm{CaC}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca(OH)}_{2} + \mathrm{C}_{2} \mathrm{H}_{2} \]From this equation, we see that the mole ratio between calcium carbide (\(\mathrm{CaC}_{2}\)) and acetylene (\(\mathrm{C}_{2}\mathrm{H}_{2}\)) is 1:1. This means that one mole of calcium carbide will produce one mole of acetylene when it reacts with water. Understanding this, you can predict the amount of product formed from a given amount of reactant.

Chemical Reaction

A chemical reaction involves the transformation of one or more substances into new substances. During this process, bonds between atoms are broken and new ones are formed, altering the arrangement of atoms.
In our given exercise, the chemical reaction:\[ \mathrm{CaC}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca(OH)}_{2} + \mathrm{C}_{2} \mathrm{H}_{2} \]illustrates how molecules of water react with calcium carbide to produce calcium hydroxide and acetylene. The reactants are calcium carbide and water, and the products are calcium hydroxide and acetylene. This reaction clearly shows the interaction and rearrangement of bonds among the contributing atoms.- Reactants: Calcium Carbide (\(\mathrm{CaC}_{2}\)) and Water (\(\mathrm{H}_{2} \mathrm{O}\))- Products: Calcium Hydroxide (\(\mathrm{Ca(OH)}_{2}\)) and Acetylene (\(\mathrm{C}_{2} \mathrm{H}_{2}\))Thus, the chemical reaction is what allows us to compute how much of a product is formed when a certain amount of reactants are used.

Calcium Carbide

Calcium carbide (\(\mathrm{CaC}_{2}\)) is a chemical compound that has significant industrial applications. It appears as a grayish-white, solid, crystalline material and is a key ingredient in the production of acetylene.
When calcium carbide reacts with water, acetylene gas is produced along with calcium hydroxide.
This interaction is not only fascinating but also highly practical:- **Properties of Calcium Carbide**: - Formula: \(\mathrm{CaC}_{2}\) - Solid at room temperature - Reactive with waterDue to its reactivity with water, calcium carbide must be stored carefully to prevent accidental reactions. It's widely used in various applications, especially in the synthesis of acetylene for welding and as a ripening agent for fruits.

Acetylene Production

Acetylene (\(\mathrm{C}_{2} \mathrm{H}_{2}\)) is a colorless gas widely used as a fuel for welding and cutting metals. It is produced industrially through the reaction of calcium carbide and water, as represented in the balanced chemical equation:\[ \mathrm{CaC}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{Ca(OH)}_{2} + \mathrm{C}_{2} \mathrm{H}_{2} \]This process is favored due to the efficiency and straightforwardness of converting calcium carbide to acetylene.- **Steps in Acetylene Production**: - React calcium carbide with water - Catch the released acetylene gas - Manage the by-product, calcium hydroxideGiven its importance in industrial and laboratory applications, an understanding of how acetylene is produced and the related chemical reaction is key. This helps in anticipating the outputs and understanding the industrial importance of both calcium carbide and acetylene gas.