Ask a New Question
Menu

In the Solvay process for the production of sodium carbonate (or washing soda), one step is the decomposition of sodium hydrogen carbonate.

2
NaHCO
3
(
𝑠
)
→
Na
2
CO
3
(
𝑠
)
+
CO
2
(
𝑔
)
+
H
2
O
(
𝑔
)
2NaHCO
3
​
(s)→Na
2
​
CO
3
​
(s)+CO
2
​
(g)+H
2
​
O(g)

When 4.3 grams of sodium hydrogen carbonate (NaHCO₃) was placed in a calorimeter and allowed to react completely, 20.0 mL of water surrounding the reaction changed temperature from 29°C to 18.3°C.

a) Calculate the molar enthalpy of decomposition of NaHCO₃ (ΔHdecomp). [6]

1 answer

To calculate the molar enthalpy of decomposition of sodium hydrogen carbonate (NaHCO₃), we need to follow these steps:

  1. Calculate the number of moles of NaHCO₃ used.
  2. Calculate the amount of heat absorbed by the water.
  3. Calculate the molar enthalpy of decomposition from the heat and moles of NaHCO₃.

Step 1: Calculate the number of moles of NaHCO₃.

The molar mass of NaHCO₃ is calculated as follows:

  • Na: 22.99 g/mol
  • H: 1.01 g/mol
  • C: 12.01 g/mol
  • O: 16.00 g/mol × 3 = 48.00 g/mol

Calculating the total: \[ \text{Molar mass of NaHCO}_3 = 22.99 + 1.01 + 12.01 + 48.00 = 84.01 , \text{g/mol} \]

Now, calculate the number of moles (\( n \)) of NaHCO₃: \[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{4.3 , \text{g}}{84.01 , \text{g/mol}} \approx 0.0511 , \text{mol} \]

Step 2: Calculate the amount of heat absorbed by the water.

To find the heat absorbed by water (\( q \)), we use: \[ q = m \cdot c \cdot \Delta T \] where:

  • \( m \) = mass of water = volume × density = 20.0 mL × 1 g/mL = 20.0 g (assuming density of water is 1 g/mL)
  • \( c \) = specific heat capacity of water = 4.18 J/g°C
  • \( \Delta T \) = change in temperature = final temperature - initial temperature = 18.3°C - 29°C = -10.7°C (the temperature decreased, so it's negative)

Now plug in the values: \[ q = 20.0 , \text{g} \cdot 4.18 , \text{J/g°C} \cdot (-10.7 , \text{°C}) \] \[ q = 20.0 \cdot 4.18 \cdot (-10.7) \approx -894.76 , \text{J} \]

(We take the absolute value since \( q \) represents the heat released from the reaction to the surroundings.)

Step 3: Calculate the molar enthalpy of decomposition.

To find the molar enthalpy of decomposition (\( \Delta H_{\text{decomp}} \)), we need to divide the heat absorbed by the number of moles of NaHCO₃.

\[ \Delta H_{\text{decomp}} = \frac{q}{n} \] \[ \Delta H_{\text{decomp}} = \frac{-894.76 , \text{J}}{0.0511 , \text{mol}} \approx -17555.53 , \text{J/mol} \]

Converting to kJ/mol (since it's common to express ΔH in kJ): \[ \Delta H_{\text{decomp}} \approx -17.56 , \text{kJ/mol} \]

Final Answer:

The molar enthalpy of decomposition of NaHCO₃ is approximately -17.56 kJ/mol.