On average, a tree produces 118 kilograms of oxygen a year. how many molecules of carbon dioxide must a tree take in each year in order to accomplish this? (don't forget to convert kilograms to grams)

a. 1.23 x 1032
b. 2.22 x 1027
c. 3.24 x 1029
d. 3688.9

1. no. of moles of Oxygen = 3687.5 mol

2. amount of CO₂ taken = 3687.5 moles

3. Option B is correct = 2.22 x 10²⁷

Explanation:

Data Given:

Amount of O₂ = 118 Kg

moles of O₂ = ?

no. of molecules of CO₂ = ?

Solution:

First we have to convert Kg to g

Convert unit from Kg to g

1 Kg = 1000 g

118 Kg = 118 x 1000 = 118000 g

Now we will find number of moles of O₂

Mole formula will be used

           no. of moles = mass in grams/ molar mass

molar mass of O₂ = 2(16) = 32 g/mol

Put values in mole formula

          no. of moles = 118000 g/ 32 g/mol

          no. of moles = 3687.5 mol

So we have  3687.5 moles of Oxygen

Part 2:

Now we have to find moles of CO₂ taken by plant to to produce 3687.5 moles of Oxygen

First we will look for the reaction by

            6 CO₂ + 6 H₂O > 6 C₆H₆O₆ + 6 O₂

So,

           6 CO₂ + 6 H₂O > 6 C₆H₆O₆ + 6 O₂

           6 mole                                                 6 mole

So from the above reaction we come to know that 6 moles of CO₂ will be taken to produce 6 moles of O₂

As we Know,

         6 moles of CO₂ ≅ 6 moles of O₂

So,

        3687.5 moles of CO₂ ≅ 3687.5 moles of O₂

So amount of CO₂ taken = 3687.5 moles

Part 3

Now we will find number of molecules of CO₂

Mole formula will be used

           no. of moles = no. of molecules / Avogadro's number

Rearrange the above formula

          no. of molecules =  no. of moles x Avogadro's number . . . . . (1)

Avogadro's number = 6.022 x 10²³

Put values in mole formula (1)

          no. of molecules =  3687.5 moles x 6.022 x 10²³

           no. of molecules =  2.22 x 10²⁷

So ,

Option B is correct = 2.22 x 10²⁷

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