Question

Calculate the mass of \(100\) molecules of oxygen in amu and in grams.

• A. \(3200\) u and \(5.314\times 10^{-21}\) g
• B. \(1600\) u and \(2.657\times 10^{-21}\) g
• C. \(32\) u and \(1.328\times 10^{-21}\) g
• D. \(8\) u and \(3.978\times 10^{-21}\) g

Hint:

One O$_2$ molecule weighs 32 u and $1\text{ u}=1.66\times10^{-24}$ g.

Answer 1

The Correct Option is A

Step 1: Use the mole route
$100$ molecules is $\frac{100}{6.022\times10^{23}}$ mol. Molar mass of O$_2$ is $32$ g/mol.
\[ m=\frac{100\times32}{6.022\times10^{23}}=5.314\times10^{-21}\text{ g} \]

Step 2: Get the mass in u
One u is $\frac{1}{6.022\times10^{23}}$ g, so $5.314\times10^{-21}$ g is $3200$ u.
Both values match option (A).

Final Answer:
Same result by moles: $3200$ u and $5.314\times10^{-21}$ g. Option (A). \[ \boxed{\text{(A)}} \]