# Anyone good at chemistry? please try this question for me.

## May 7, 2017

13.31 days

#### Explanation:

Assume the reaction is independent of the concentration of the reactant (i.e. a constant reaction rate or zero-order reaction) and the balanced chemical reaction is as follows:

C6H12O6 ---> 2C2H5OH + 2CO2

First, you need to find the amount of ethanol that has reacted in 5 hours. I will work in grams and mol for consistency.

$n \left(e t h a n o l\right) = \frac{m}{M} = \frac{8000}{46} = 173.91$ mol

Using the stoichiometric ratios of 1:2 (glucose:ethanol) in the chemical reaction, it can be seen that one glucose molecule will be converted to two ethanol molecules. This means the amount of glucose molecules used in 5 hours is half the amount of ethanol molecules produced.

$\text{n(glucose)} = 0.5 \cdot 173.91 = 86.96$ $m o l$

Next, we need the mass of glucose used in 5 hours.

$\text{mass(glucose)} = n \cdot M = 86.96 \cdot 180 = 15652.17$ $g$

The rate of the reaction is obtained by dividing the mass of glucose that reacted by the time it took.

$\text{rate of glucose consumption} = \frac{15652.17}{5} = 3130.43$ $\text{g"/"hr}$

Now, for the 1000 kg, we know the rate and we know the mass of glucose that reacts, so we can use some algebra to solve for the number of hours. The rate multiplied by the number of hours gives the mass reacted.

$3130.43$ $\text{g"/"hr}$ $\cdot x$ $\text{hr}$$= 1000 \cdot {10}^{3}$ $g$

With only one unknown, we can rearrange and solve for x.

$\text{x} = {10}^{6} / 3130.43 = 319.44$ $\text{hours}$

To convert to days, divide by 24.

$\frac{319.44}{24} = 13.31$ $\text{days}$