Q. 7.109 - An Introduction to General, Organic, and Biological Chemistry

Question

At a winery, glucose (${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$) in grapes undergoes fermentation to produce ethanol (${\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}$) and carbon dioxide. ($7.8$)

$$\begin{gathered} {\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6\left(\mathrm{aq}\right)\to 2{\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}\left(\mathrm{aq}\right) + 2{\mathrm{CO}}_2\left(\mathrm{g}\right) \\ \mathrm{Glucose} \mathrm{Ethanol} \end{gathered}$$

Glucose in grapes ferments to produce ethanol.

a. How many grams of glucose are required to form $124$ g of ethanol? 

b. How many grams of ethanol would be formed from the reaction of $0.240$ kg of glucose?

Step-by-Step Solution

Answer

(a) The $242$ g of glucose are required to form $124$ g of ethanol

(b) The $123$ g of ethanol would be formed from the reaction of $0.240$ kg of glucose

Part (a) Step 1: Given information

We need to find the mass of glucose required to form $124$ g of ethanol

Part (a) Step 2: Explanation

From the given reaction i.e. ${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6\to 2{\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}+2{\mathrm{CO}}_2$

We know that 

The $92$ g of ethanol is formed by $180$ g of glucose

Therefore, $124$ g of ethanol is formed by $\frac{180 \cancel{\mathrm{g}}}{92 \cancel{\mathrm{g}}}\times 124 \mathrm{g}=242 \mathrm{g}$

Part (b) Step 1: Given information

We need to find the mass of ethanol would be formed from the reaction of $0.240$ kg of glucose 

Part (b) Step 2: Explanation

From part (a) 

We know that

The $180$ g of glucose produces $92$ g of ethanol

Therefore, $0.240$ kg of glucose produces $\frac{92 \cancel{\mathrm{g}}}{180 \cancel{\mathrm{g}}}\times 0.240 \mathrm{kg}=0.123 \mathrm{kg}=123 \mathrm{g}$