if 32kj of energy results in an average weight gain of 1 g of body mass, then how much weight could a person gain after eating 1 cookie. use dimensional analysis

mass of 15.21g of a cookie.

If we really want to get down to brass tacks, eating something with a mass of 1 g increases the body mass by 1 g. Eating something with a mass of 10 g increases the body mass by 10 g (perhaps not permanently but shortly after eating). And I don't need dimensional analysis to tell me that. So I would say eating a cooking with a mass of 15.21 g will increase the body mass by 15.21 g. The only other option I see is for you to consider the cookie as 100% sucrose, look up or calculate the energy/mole, convert to 15.21 g sucrose and then to kJ and grams. Since this is a bonus question, could this be a case of the kJ energy etc being a red herring?

once i have the amount of mols of sucrose present how do i convert that to sucrose? and to kj and grams?

lets say i have 0.03110 mols of sucrose

To answer this question using dimensional analysis, we will follow the steps below:

Step 1: Identify the given values and units:
- Energy gained from 1 cookie: 32 kJ
- Weight gain from 32 kJ: 1 g
- Mass of 1 cookie: 15.21 g

Step 2: Set up the conversion factor:
We know that 32 kJ of energy results in a weight gain of 1 g. Therefore, the conversion factor is 1 g / 32 kJ.

Step 3: Set up the calculation using dimensional analysis:
We can multiply the given mass of the cookie (15.21 g) by the conversion factor to find the weight gain from eating 1 cookie.

15.21 g * (1 g / 32 kJ)

Step 4: Convert units:
In order to use the conversion factor, we need to convert the energy value to the same unit as the conversion factor, which is kilojoules (kJ). Let's convert 15.21 g of cookie to kilojoules (kJ).

To perform this conversion, we need to consider the nutritional information and determine the energy content (in kJ) per gram (g) of the cookie.

Step 5: Consult nutritional information:
Typically, nutritional information lists the energy content in kilocalories (kcal) per gram (g) of the food. To convert from kilocalories to kilojoules, we need to multiply by 4.184.

Let's assume the energy content of the cookie is 5.5 kcal/g. We then convert this to kJ/g by multiplying by 4.184.

Step 6: Calculate the weight gain:
Now that we have the energy content per gram of the cookie in kilojoules, we can substitute this value into our dimensional analysis calculation:

15.21 g * (1 g / 32 kJ) * (5.5 kcal/g * 4.184 kJ/kcal)

After performing the calculation, the units will cancel out, leaving us with the weight gain in grams (g).