Questions: How much energy is evolved or absorbed as heat if 8.50 kg of Ca(OH)2 reacts with a stoichiometric amount of CO2? Heat = k

Transcript text: (b) How much energy is evolved or absorbed as heat if 8.50 kg of $\mathrm{Ca}(\mathrm{OH})_{2}$ reacts with a stoichiometric amount of $\mathrm{CO}_{2}$ ? Heat $=$ $\square$ k] Submit

Solution

Solution Steps

Step 1: Write the balanced chemical equation

The reaction between calcium hydroxide and carbon dioxide is: \[ \mathrm{Ca(OH)_2} + \mathrm{CO_2} \rightarrow \mathrm{CaCO_3} + \mathrm{H_2O} \]

Step 2: Determine the molar masses

Calculate the molar masses of the reactants:

$ \mathrm{Ca(OH)_2} $: $ 40.08 + 2 \times (16.00 + 1.01) = 74.10 \, \text{g/mol} $
$ \mathrm{CO_2} $: $ 12.01 + 2 \times 16.00 = 44.01 \, \text{g/mol} $

Step 3: Convert mass to moles

Convert the given mass of $ \mathrm{Ca(OH)_2} $ to moles: \[ \text{Moles of } \mathrm{Ca(OH)_2} = \frac{8500 \, \text{g}}{74.10 \, \text{g/mol}} = 114.7 \, \text{mol} \]

Step 4: Use stoichiometry to find moles of $ \mathrm{CO_2} $

From the balanced equation, 1 mole of $ \mathrm{Ca(OH)_2} $ reacts with 1 mole of $ \mathrm{CO_2} $. Therefore, moles of $ \mathrm{CO_2} $ required: \[ \text{Moles of } \mathrm{CO_2} = 114.7 \, \text{mol} \]

Step 5: Calculate the heat evolved or absorbed

Assume the enthalpy change ($ \Delta H $) for the reaction is known (e.g., $-113.8 \, \text{kJ/mol}$ for the formation of $ \mathrm{CaCO_3} $ from $ \mathrm{Ca(OH)_2} $ and $ \mathrm{CO_2} $). The total heat evolved or absorbed: \[ \text{Heat} = 114.7 \, \text{mol} \times (-113.8 \, \text{kJ/mol}) = -13055.86 \, \text{kJ} \]

Step 6: Report the final value

The energy evolved as heat is: \[ \boxed{-13055.86 \, \text{kJ}} \]