Question

1 g of dry green algae absorb 4.7$ \times {10^{ - 3}}$ moles of $C{O_2}$ per hour by photosynthesis. If the fixed carbon atom after photosynthesis is stored in the form of starch (${C_6}{H_{10}}{O_5}$) Cal. How much time will it take algae to double its own weight ?

Answer 1

Hint: In the question, the rate of absorption of carbon dioxide by the algae is provided. And even the amount required is also given. We need to find the moles of carbon needed to fix and then by dividing the moles by absorption rate, we will get the time taken by the green algae.

Complete Solution :
Let us first write what is given and what we need to find out and then move step by step to get an answer.
Given :
Mass of dry green algae = 1 g
Absorption rate of algae = 4.7$ \times {10^{ - 3}}$ moles of $C{O_2}$ per hour

To find :
Time taken by algae to double its own weight
So, we need to find the time taken by algae to get 1 g weight.
The starch has molecular formula - ${C_6}{H_{10}}{O_5}$
As the Carbon dioxide is fixed in the form of starch. So, we need to find out the time taken for the formation of 1 g of starch.
Molar mass of starch = 162 g

The reaction is -
$C{O_2} \to {({C_6}{H_{10}}{O_5})_n}$
We know that moles of Carbon in $C{O_2}$ = 6n $ \times $ moles of Carbon in ${({C_6}{H_{10}}{O_5})_n}$ = 6 $ \times \dfrac{1}{{n(162)}}$
So, moles of carbon dioxide required = $\dfrac{6}{{162}}$
moles of carbon dioxide required = 0.037 moles
Rate of absorption = 4.7$ \times {10^{ - 3}}$ moles/ hr
Time (hr) = $\dfrac{{0.037}}{{4.7 \times {{10}^{ - 3}}}}$
Time (hr) = 7.88 hr

Note: It must be noted that green plants make their own food by the process of photosynthesis. In this process, green plants take up carbon dioxide and water from the atmosphere and in the presence of sunlight, convert it into starch. This starch is the stored food.