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. ($7.8$)

localid="1652639320991" $$\begin{gathered} {\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6\left(\mathrm{aq}\right)\to 2{\mathrm{C}}_2{\mathrm{H}}_6\mathrm{O}\left(\mathrm{aq}\right)+2{\mathrm{CO}}_2\left(\mathrm{g}\right) \\ \mathrm{Glucose}\mathrm{Ethanol} \end{gathered}$$

Glucose in grapes ferments to produce ethanol.

a. How many grams of glucose are required to form localid="1653473342835" $124$gof ethanol?

b. How many grams of ethanol would be formed from the reaction of localid="1653473362281" $0.240$kgof glucose?

Short answer

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

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

Step-by-step solution

Part (a) Step 1: Given information

We need to find the mass of glucose required to form$124$gof 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 localid="1653473457616" $92$g of ethanol is formed by localid="1653473474734" $180$g of glucose

Therefore, localid="1653473489746" $124$gof ethanol is formed by localid="1653485279413" $\frac{180\cancel{\mathrm{g}}}{92\cancel{\mathrm{g}}}\times 124\mathrm{g}=242\mathrm{g}$

Part (b) Step 1: Given information

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

Part (b) Step 2: Explanation

From part (a)

We know that

The $180$gof glucose produces $92$gof ethanol

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