Please help me with this question from my homework package
What is the minimum number of photons with wavelength 645nm needed to prepare 135 grams of glucose?
When the thermochemical equation is
C6H12O6(s)+ 6O2(g)--> 6CO2(g)+ 6H2O(g) Reaction is -2539.01 Kj/mol
How much energy is needed for a photon of 645 nm? That is delta E = hc/wavelength - 6.626 x 10^-34*3 x 10^8/645 x 10^-9 = about 3 x 10^-19 J/photon (but you need to do this exactly).
How much energy is needed to prepare 135 g glucose? That will be 135/180 (you need to convert the molar mass exactly since my 180 is an estimate) = about 0.75 mol glucose so 0.75 x 2539.01 x 10^3 J/mol = about 1904 J.
So how many packets of energy of 3 x 10^-19 do you need to have a total of 1904 J? Check my work.
To determine the minimum number of photons needed to prepare a certain amount of glucose, we need to employ the concept of stoichiometry.
First, we must calculate the amount of glucose in moles using the given mass of 135 grams and its molar mass. The molar mass of glucose (C6H12O6) can be calculated by summing the atomic masses of its constituent elements.
Next, we use the balanced thermochemical equation to determine the molar ratio between glucose and photons. From the equation, we can see that for every mole of glucose produced, the reaction requires a certain number of photons.
Finally, with the molar ratio and the mole quantity of glucose, we can calculate the minimum number of photons needed by multiplying the mole quantity of glucose by the molar ratio.
Let's perform the calculations step by step:
1. Calculate the molar mass of glucose (C6H12O6):
- Carbon (C) has a molar mass of 12.01 g/mol.
- Hydrogen (H) has a molar mass of 1.01 g/mol.
- Oxygen (O) has a molar mass of 16.00 g/mol.
- The molar mass of glucose = (6 * C) + (12 * H) + (6 * O)
2. Use the calculated molar mass to find the moles of glucose in 135 grams. Divide the given mass by the molar mass of glucose.
3. Determine the molar ratio of photons to glucose from the balanced thermochemical equation. From the equation, we can see that the ratio is not explicitly given. However, we can infer the ratio based on the reaction stoichiometry. For every mole of glucose produced in the reaction, a fixed number of photons are absorbed.
4. Finally, multiply the moles of glucose by the molar ratio to calculate the minimum number of photons needed.
Please provide the molar mass of glucose, and we can continue with the calculations.