Question

The source of bitterness in dark chocolate is the compound theobromine, an alkaloid present in cocoa beans. In a sample of dark chocolate there are 6.72×1020 molecules of theobromine present. How many milligrams of theobromine are present in the sample? The molecular formula for theobromine is C7H8N4O2.

Answer 1

Answer:
`1.98* 10^(-4)` mg

Explanation:-

According to avogadro's law, 1 mole of every substance occupies 22.4 Liters at STP , contains avogadro's number
`6.023* 10^(23)` of particles and weigh equal to the molecular mass of the substance.

To calculate the moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given molecules}}{\text {Avogadro's number}}`

`\text{Number of moles}=(6.72* 10^(20))/(6.023* 10^(23))=1.1* 10^(-3)moles`

Now 1 mole of
`C_7H_8N_4O_2` molecule weigh = 180g

`1.1* 10^(-3)moles` of
`C_7H_8N_4O_2` molecule weigh =
`(180)/(1)* 1.1* 10^(-3)=0.198g=1.98* 10^(-4)mg` (1g=1000mg)

Thus
`1.98* 10^(-4)` mg of theobromine are present in the sample.