93. a sugar crystal contains approximately 1.8×10^17 sucrose (c12h22o11) molecules. what is its mass in mg?

Explanation:

Step1: Calculate molar mass of sucrose

The molar mass of $C_{12}H_{22}O_{11}$: $M=(12\times12.01 + 22\times1.01+11\times16.00)\ g/mol$ $M=(144.12 + 22.22+176.00)\ g/mol$ $M = 342.34\ g/mol$

Step2: Use Avogadro's number to find moles

Avogadro's number $N_A = 6.022\times 10^{23}\ molecules/mol$. The number of moles $n$ of sucrose is $n=\frac{N}{N_A}$, where $N = 1.8\times 10^{17}$ molecules. $n=\frac{1.8\times 10^{17}}{6.022\times 10^{23}}\ mol\approx2.99\times 10^{-7}\ mol$

Step3: Calculate mass in grams

Using the formula $m = n\times M$, where $n$ is the number of moles and $M$ is the molar - mass. $m=(2.99\times 10^{-7}\ mol)\times342.34\ g/mol\approx1.02\times 10^{-4}\ g$

Step4: Convert grams to milligrams

Since $1\ g = 1000\ mg$, then $m=(1.02\times 10^{-4}\ g)\times1000\ mg/g = 0.102\ mg$

Answer:

$0.102\ mg$