Question

1 g of dry green algae absorbs $4.7\times {10}^{-3}$ mol of $C{O}_2$ per hour by photosynthesis. If the fixed carbon atom are stored as starch ($C_6{H}_{10}{O}_5{)}_n$, how long would it take for the algae to double their own weight assuming photosyntheseis takes place at constant rate?
Give the answer to nearest integer.

Answer 1

Given, absorption rate of $C{O}_2$ = $4.7\times {10}^{-3}$/hr by 1 g of algae and forming starch
So, mass of algae will be doubled if it forms 1 g of starch
Mass of ($C_6{H}_{10}{O}_5{)}_n$ = 1 g
molar mass of starch = 162n
$C{O}_2$ gas will be converted into starch (($C_6{H}_{10}{O}_5{)}_n$)
Using POAC for carbon atom
mole of C in $C{O}_2$ consumed = moles of C in ($C_6{H}_{10}{O}_5{)}_n$
Moles of C in $C{O}_2$ = 6n $\frac{1}{162n}$
moles of $C{O}_2$ required = $\frac{6}{162}$ mol
Time of absorption = $\frac{6/162}{4.7\times {10}^{-3}}$ = 7.88 hours