Problem 135 - Chemistry

Question

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) can be made by combining calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) with water. (a) Write an equation for the reaction. (b) What is the maximum amount of heat (in joules) that can be obtained from the combustion of acetylene, starting with \(74.6 \mathrm{~g}\) of \(\mathrm{CaC}_{2} ?\)

Step-by-Step Solution

Answer

The maximum heat from the combustion is -1512200 J.

Step 1: Write the Balanced Chemical Equation

Start by writing the chemical equation for the reaction between calcium carbide and water to form acetylene and calcium hydroxide. \[ \mathrm{CaC}_{2} + 2\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{C}_{2}\mathrm{H}_{2} + \mathrm{Ca(OH)_{2}} \] This equation shows that one mole of calcium carbide reacts with two moles of water to produce one mole of acetylene and one mole of calcium hydroxide.

Step 2: Calculate Moles of Calcium Carbide

Find the molar mass of calcium carbide (\(\mathrm{CaC}_{2}\)). The atomic masses are approximately: Ca = 40.08 g/mol, C = 12.01 g/mol. Thus, \[ \mathrm{Molar\ mass\ of\ CaC}_{2} = 40.08 + 2 \times 12.01 = 64.1\, \mathrm{g/mol} \]Now calculate the moles of \(\mathrm{CaC}_{2}\) from the given mass (74.6 g):\[ \text{moles of } \mathrm{CaC}_{2} = \frac{74.6 \text{ g}}{64.1 \text{ g/mol}} \approx 1.164\, \text{mol} \]

Step 3: Combustion of Acetylene

Write the equation for the combustion of acetylene:\[ \mathrm{2C_{2}H_{2} + 5O_{2} \rightarrow 4CO_{2} + 2H_{2}O} \]This reaction shows that 2 moles of \( \mathrm{C_{2}H_{2}} \) produce 4 moles of \( \mathrm{CO_{2}} \) and 2 moles of \( \mathrm{H_{2}O} \) upon combustion.

Step 4: Calculate Heat from Combustion

The standard enthalpy change for the combustion of acetylene is \(-1300\, \mathrm{kJ/mol}\) of \(\mathrm{C_{2}H_{2}}\). Since 1 mole of \(\mathrm{CaC}_{2}\) produces 1 mole of \(\mathrm{C_{2}H_{2}}\), we use the number of moles calculated in Step 2:\[ \mathrm{Heat\ released} = 1.164\, \mathrm{mol} \times (-1300\, \mathrm{kJ/mol}) = -1512.2\, \mathrm{kJ} \]Convert \(-1512.2\, \mathrm{kJ}\) to \(\mathrm{J} \) (since 1 kJ = 1000 J):\[ -1512.2\, \mathrm{kJ} \times 1000 = -1512200\, \mathrm{J} \]

Step 5: State the Final Answer

The maximum amount of heat obtainable from the combustion of acetylene, starting with \(74.6\, \mathrm{g}\) of \(\mathrm{CaC}_{2}\), is \(-1512200\, \mathrm{J}\) or \(-1512.2\, \mathrm{kJ}\).

Key Concepts

Chemical Reaction Equation

A chemical reaction equation is a symbolic representation of a chemical reaction. It shows the reactants and products, as well as their quantities and states. The importance of a balanced equation lies in the law of conservation of mass, ensuring the same number of each type of atom on both sides of the equation.
For the production of acetylene using calcium carbide and water, the balanced chemical equation is:\[ \mathrm{CaC}_{2} + 2\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{C}_{2}\mathrm{H}_{2} + \mathrm{Ca(OH)_{2}}\]

• The reactants include calcium carbide \(\mathrm{CaC}_2\) and water \(\mathrm{H}_2\mathrm{O}\).
• The products are acetylene \(\mathrm{C}_2\mathrm{H}_2\) and calcium hydroxide \(\mathrm{Ca(OH)_2}\).

This equation indicates that one mole of calcium carbide reacts with two moles of water to yield one mole of acetylene and one mole of calcium hydroxide. Remember, balancing chemical equations ensures a proper stoichiometric relationship, crucial for understanding reaction details and energy changes.

Moles Calculation

Moles calculation is a method used to quantify the amount of substances involved in a chemical reaction. The basic idea involves determining how many "particles" (like atoms or molecules) are in a given mass.
Conversion from mass to moles entails using the molar mass, which is the mass of one mole of a substance. Here's a brief guide on how to calculate:

• Determine the molar mass of the compound (add up the atomic masses of all atoms in the compound).
• Use the formula: \(\text{moles} = \frac{\text{given mass}}{\text{molar mass}}\).

For calcium carbide \(\mathrm{CaC}_2\), the molar mass is calculated as:\[ \mathrm{Molar\ mass}\ (\mathrm{CaC}_{2}) = 40.08 \frac{\mathrm{g}}{\mathrm{mol}} + 2 \times 12.01 \frac{\mathrm{g}}{\mathrm{mol}} = 64.1 \frac{\mathrm{g}}{\mathrm{mol}} \]Given 74.6 g of \(\mathrm{CaC}_2\), the moles are calculated as:\[ \text{moles of } \mathrm{CaC}_2 = \frac{74.6 \text{ g}}{64.1 \text{ g/mol}} \approx 1.164 \text{ moles} \]This calculation is fundamental for further predicting amounts and energy changes in the reaction.

Enthalpy Change

Enthalpy change, denoted as \(\Delta H\), refers to the heat change at constant pressure in a chemical process. It's either absorbed (endothermic) or released (exothermic). For combustion reactions, like that of acetylene, the standard enthalpy change indicates heat release, valuing it in energy units such as kilojoules per mole (kJ/mol).
In our case, the combustion equation:\[2 \mathrm{C_{2}H_{2}} + 5 \mathrm{O_{2}} \rightarrow 4 \mathrm{CO_{2}} + 2 \mathrm{H_{2}O}\]shows that the combustion of acetylene has an enthalpy change \(-1300\, \mathrm{kJ/mol}\) of \(\mathrm{C_{2}H_{2}}\). Given 1.164 moles of acetylene (from our moles calculation), the total energy released is:\[ \mathrm{Heat\ released} = 1.164 \times (-1300) = -1512.2\, \mathrm{kJ} = -1512200\, \mathrm{J}\]Converting kilojoules to joules is simple through multiplying by 1000, providing the final heat outcome attained in the reaction. Understanding enthalpy change is essential for energy anticipation in chemical transformations.

Chemical Stoichiometry

Chemical stoichiometry is the mathematical relationship between reactants and products in a chemical reaction. It involves using mole ratios derived from a balanced chemical equation to predict the quantities of reactants and products.
For the acetylene combustion reaction:\[ \mathrm{2C_{2}H_{2} + 5O_{2} \rightarrow 4CO_{2} + 2H_{2}O}\]The stoichiometry suggests:

• 2 moles of \(\mathrm{C_{2}H_{2}}\) react with 5 moles of \(\mathrm{O_{2}}\)
• Produce 4 moles of \(\mathrm{CO_{2}}\) and 2 moles of \(\mathrm{H_{2}O}\)

This reaction stoichiometry indicates that each mole of \(\mathrm{CaC}_{2}\) results in one mole of acetylene, translating to an equivalent heat release correlation. Consequently, stoichiometric analysis guides precise predictions and formulas in chemical manipulations, ensuring efficiency and accuracy in real-world applications. Understanding stoichiometry is integral to grasping the essence of chemical reactions and their corresponding implications.