Photosysthesis is a bio process by which plants make energy rich molecules from low energy molecules with the help of energy from sunlight . The photosysthesis of glucose can be represented as:
`6CO_(2(g))+ 6H_(2)O_(g) + hv rarr C_(5)H_(12)O_(6(s)) + 6O_(2)(g)..........(i)`
The energy of one mole of a photon of wave lenght is known as one Einstein.
On an average , solar radiation `7 xx 10^(14)` kg of glucose annually on earth . Calculate the annual decrease in the `CO_(2)` level in the troposphere in ppm , due to photosynthesis. (1 ppm=1 g of `CO_(2)` per `10^(3)` kg of air in troposhere). Assume that the total mass of air envolope surrounding the earth is `5.0 xx 10^(15)` kg and 80% of its is present in the tropsphere.

Answer

To solve the problem of calculating the annual decrease in the CO₂ level in the troposphere due to photosynthesis, we will follow these steps:

### Step 1: Calculate the moles of glucose produced annually
Given that the annual solar radiation results in the production of \(7 \times 10^{14}\) kg of glucose, we first convert this mass into grams:
\[ \text{Mass of glucose} = 7 \times 10^{14} \text{ kg} = 7 \times 10^{17} \text{ g} \]

Next, we calculate the number of moles of glucose produced. The molar mass of glucose (\(C_6H_{12}O_6\)) is approximately 180 g/mol. Therefore, the number of moles of glucose (\(n_{\text{glucose}}\)) can be calculated as:
\[ n_{\text{glucose}} = \frac{\text{mass of glucose}}{\text{molar mass of glucose}} = \frac{7 \times 10^{17} \text{ g}}{180 \text{ g/mol}} \approx 3.89 \times 10^{15} \text{ mol} \]

### Step 2: Calculate the moles of CO₂ consumed
From the balanced equation of photosynthesis:
\[ 6 \text{CO}_2 + 6 \text{H}_2O + \text{hv} \rightarrow C_6H_{12}O_6 + 6 \text{O}_2 \]
We see that 6 moles of CO₂ are consumed for every mole of glucose produced. Thus, the moles of CO₂ consumed (\(n_{\text{CO}_2}\)) is:
\[ n_{\text{CO}_2} = n_{\text{glucose}} \times 6 = 3.89 \times 10^{15} \text{ mol} \times 6 \approx 2.33 \times 10^{16} \text{ mol} \]

### Step 3: Calculate the mass of CO₂ consumed
The molar mass of CO₂ is approximately 44 g/mol. Therefore, the total mass of CO₂ consumed (\(W_{\text{CO}_2}\)) is:
\[ W_{\text{CO}_2} = n_{\text{CO}_2} \times \text{molar mass of CO}_2 = 2.33 \times 10^{16} \text{ mol} \times 44 \text{ g/mol} \approx 1.025 \times 10^{18} \text{ g} \]

### Step 4: Calculate the total mass of air in the troposphere
The total mass of the air envelope surrounding the Earth is given as \(5.0 \times 10^{15}\) kg, and 80% of this is in the troposphere:
\[ \text{Mass of air in troposphere} = 5.0 \times 10^{15} \text{ kg} \times 0.8 = 4.0 \times 10^{15} \text{ kg} = 4.0 \times 10^{18} \text{ g} \]

### Step 5: Calculate the decrease in CO₂ level in ppm
Since 1 ppm is defined as 1 g of CO₂ per \(10^3\) kg of air, we can find the decrease in CO₂ level in ppm:
\[ \text{Decrease in CO}_2 \text{ level (ppm)} = \frac{W_{\text{CO}_2}}{\text{mass of air in troposphere} / 10^3} \]
Substituting the values:
\[ \text{Decrease in CO}_2 \text{ level (ppm)} = \frac{1.025 \times 10^{18} \text{ g}}{4.0 \times 10^{15} \text{ kg} / 10^3} = \frac{1.025 \times 10^{18}}{4.0 \times 10^{12}} \approx 2.56 \times 10^{5} \text{ ppm} \]

### Final Answer
The annual decrease in the CO₂ level in the troposphere due to photosynthesis is approximately \(2.56 \times 10^{5}\) ppm.