According to photosynthesis equation, how much solar energy consume when a plant to produce 180g glucose and 193g `O_2`

Options

A. 67.72 kcal
B. 677.2 calories
C. 677.2 kcal
D. 686 calories

Answer

To solve the problem of how much solar energy is consumed when a plant produces 180 grams of glucose and 193 grams of oxygen, we can follow these steps:

### Step 1: Understand the Photosynthesis Equation
The overall equation for photosynthesis is:
\[ 6CO_2 + 6H_2O + \text{solar energy} \rightarrow C_6H_{12}O_6 + 6O_2 \]

This indicates that 6 molecules of carbon dioxide and 6 molecules of water, in the presence of solar energy, produce one molecule of glucose and six molecules of oxygen.

### Step 2: Calculate Moles of Glucose Produced
The molecular formula of glucose is \( C_6H_{12}O_6 \). The molar mass of glucose can be calculated as follows:
- Carbon (C): 12 g/mol × 6 = 72 g/mol
- Hydrogen (H): 1 g/mol × 12 = 12 g/mol
- Oxygen (O): 16 g/mol × 6 = 96 g/mol

Total molar mass of glucose:
\[ 72 + 12 + 96 = 180 \text{ g/mol} \]

Since 180 grams of glucose corresponds to 1 mole of glucose, we have:
\[ 1 \text{ mole of glucose} \]

### Step 3: Calculate Moles of Oxygen Produced
The molar mass of oxygen (O2) is:
- Oxygen (O): 16 g/mol × 2 = 32 g/mol

To find the number of moles in 193 grams of oxygen:
\[ \text{Moles of } O_2 = \frac{193 \text{ g}}{32 \text{ g/mol}} \approx 6.03125 \text{ moles} \]

### Step 4: Relate Energy to Moles of Glucose and Oxygen
From the photosynthesis equation, we know that:
- 1 mole of glucose produces 6 moles of oxygen.
- The energy released during photosynthesis for 1 mole of glucose is approximately 677.2 kilocalories.

### Step 5: Calculate Energy Consumed
Since producing 1 mole of glucose consumes 677.2 kilocalories of solar energy, we can conclude:
- The energy consumed to produce 180 grams of glucose (1 mole) is:
\[ 677.2 \text{ kilocalories} \]

### Final Answer
Thus, the amount of solar energy consumed when a plant produces 180 grams of glucose and 193 grams of oxygen is **677.2 kilocalories**.

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