Question

Citric acid $\left({\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{8}}{\mathbf{O}}_{\mathbf{7}}\right)$is made by fermentation of sugars such as sucrase$\left({\mathbf{C}}_{\mathbf{12}}{\mathbf{H}}_{\mathbf{22}}{\mathbf{O}}_{\mathbf{11}}\right)$ in air. Oxygen is consumed and water generated as a by product

a. Write a balanced equation for the overall reaction that occurs in the manufacture of citric acid from sucrase

b. What mass of citric acid is made from 15.0kg sucrase?

Short answer

a. Balanced equation for the overall reaction is

$C_{12}{H}_{22}{O}_{11}+3O_2\to 2C_6{H}_8{O}_7+3H_{2}O$

b.Mass of citric acid made from 15 kg sucrose is 16.8kg.

Step-by-step solution

Chemical reaction

Reaction between surcease and oxygen givesCitric acid and water

The unbalanced equation is

$C_{12}{H}_{22}{O}_{11}+O_2\to C_6{H}_8{O}_7+H_{2}O$

Balancing chemical equation

• To balance ‘c’ atom on both the side, coefficient of$C_6{H}_8{O}_7$ must be 2 to balance 1 coefficient of$C_{12}{H}_{22}{O}_{11}$

$C_{12}{H}_{22}{O}_{11}+O_2\to 2C_6{H}_8{O}_7+H_{2}O$

• There are 22 H atoms on left side. To balance H atoms, we will place a coefficient of 3 for$H_{2}O$
• To balance O atom coefficient on left side is 3

$C_{12}{H}_{22}{O}_{11}+3O_2\to 2C_6{H}_8{O}_7+3H_{2}O$

Balanced Chemical equation of the reaction

Mass of Citric Acid made

According to balanced equation

One mole of sucroseproduces two moles of Citric Acid. So, amount of Citric Acid produced from 15.0kg sucrose is:

$$\begin{gathered} \left(15\times {10}^{3}g{C}_{12}{H}_{22}{O}_{11}\right)\times \frac{1mol{C}_{12}{H}_{22}{O}_{11}}{342.17g{C}_{12}{H}_{22}{O}_{11}}\times \frac{2mol{C}_6{H}_8{O}_7}{1mol{C}_{12}{H}_{22}{O}_{11}}\times \frac{192.06g{C}_6{H}_8{O}_7}{1mol{C}_6{H}_8{O}_7} \\ =16.8\times {10}^{3}g{C}_6{H}_8{O}_7=16.8kg{C}_6{H}_8{O}_7 \end{gathered}$$

Hence mass of Citric Acid produced in the reaction is 16.8kg