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Question: Enzymes convert glucose ($M$ = 180.2) to ethanol ($M$ = 46.1) according to the equation. $C_6H_{12}...

Enzymes convert glucose (MM = 180.2) to ethanol (MM = 46.1) according to the equation.

C6H12O6→2C2H5OH+2CO2C_6H_{12}O_6 \rightarrow 2C_2H_5OH + 2CO_2. What is the maximum mass of ethanol that can be made from 15.5 kg of glucose?

A

0.256 kg

B

0.512 kg

C

3.96 kg

D

7.93 kg

Answer

7.93 kg

Explanation

Solution

The balanced chemical equation is: C6H12O6→2C2H5OH+2CO2C_6H_{12}O_6 \rightarrow 2C_2H_5OH + 2CO_2

  1. Convert the mass of glucose from kg to g:

    15.5 kg×1000 g/kg=15500 g15.5 \text{ kg} \times 1000 \text{ g/kg} = 15500 \text{ g}

  2. Calculate the moles of glucose:

    Moles of glucose=15500 g180.2 g/mol=86.01 mol\text{Moles of glucose} = \frac{15500 \text{ g}}{180.2 \text{ g/mol}} = 86.01 \text{ mol}

  3. Determine the moles of ethanol produced:

    From the balanced equation, 1 mole of glucose produces 2 moles of ethanol.

    Moles of ethanol=2×86.01 mol=172.02 mol\text{Moles of ethanol} = 2 \times 86.01 \text{ mol} = 172.02 \text{ mol}

  4. Calculate the mass of ethanol:

    Mass of ethanol=172.02 mol×46.1 g/mol=7930.12 g\text{Mass of ethanol} = 172.02 \text{ mol} \times 46.1 \text{ g/mol} = 7930.12 \text{ g}

  5. Convert the mass of ethanol from g to kg:

    Mass of ethanol=7930.12 g1000 g/kg=7.93 kg\text{Mass of ethanol} = \frac{7930.12 \text{ g}}{1000 \text{ g/kg}} = 7.93 \text{ kg}

Therefore, the maximum mass of ethanol that can be made from 15.5 kg of glucose is approximately 7.93 kg.