Question

Not only due trees "fix" carbon but so do green vegetables. Photosynthesis in spinach leaves produces glucose via the Calvin cycle which involves the fixation of CO2 with ribulose 1-5 bisphosphate to form 3-phosphoglycerate via C3H8P2011(aq) + H2O(aq) + CO2(g) → 2 CzH4PO3(aq) + 2 H+(aq) If 15.0 g of 3-phosphoglycerate is formed by this reaction at T = 298 K and P = 1.00 atm what volume of CO2 is fixed? [1.00 L]

Answer 1

Answer : The volume of
`CO_2` gas is 1.00 L

Explanation :

First we have to determine the moles of
`C_3H_4PO_7^(3-)`.

Molar mass of
`C_3H_4PO_7^(3-)` = 182.9 g/mole

`\text{ Moles of }C_3H_4PO_7^(3-)=\frac{\text{ Mass of }C_3H_4PO_7^(3-)}{\text{ Molar mass of }C_3H_4PO_7^(3-)}=(15.0g)/(182.9g/mole)=0.0820moles`

Now we have to calculate the moles of
`CO_2`.

The given balanced chemical reaction is:

`C_5H_8P_2O_(11)^(4-)(aq)+H_2O(aq)+CO_2(g)\rightarrow 2C_3H_4PO_7^(3-)(aq)+2H^+(aq)`

From the reaction we conclude that,

As, 2 moles of
`C_3H_4PO_7^(3-)` produce from 1 mole of
`CO_2`

So, 0.0820 moles of
`C_3H_4PO_7^(3-)` produce from
`(0.0820)/(2)=0.041moles` of
`CO_2`

Now we have to calculate the volume of
`CO_2` gas.

Using ideal gas equation:

`PV=nRT`

where,

P = pressure of gas = 1.00 atm

V = volume of gas = ?

T = temperature of gas = 298 K

n = number of moles of gas = 0.041 mole

R = gas constant = 0.0821 L.atm/mole.K

Now put all the given values in the ideal gas equation, we get:

`(1.00atm)* V=(0.041mole)* (0.0821L.atmK^(-1)mol^(-1))* (298K)`

`V=1.00L`

Therefore, the volume of
`CO_2` gas is 1.00 L