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: Mass of one molecule
The molecular mass of O\(_2\) is \(2\times16=32\) u, so one molecule has a mass of 32 u.

Step 2: Mass of 100 molecules in u
\[ 100\times32\text{ u}=3200\text{ u} \]

Step 3: Convert to grams
Use \(1\text{ u}=1.66\times10^{-24}\) g.
\[ 3200\times1.66\times10^{-24}=5.31\times10^{-21}\text{ g} \]

Step 4: Check options
Option (A) gives \(3200\) u and \(5.314\times10^{-21}\) g. Options (B) to (D) use wrong masses (\(1600\), \(32\), \(8\) u), so they fail.

Final Answer:
The mass is 3200 u or \(5.314\times10^{-21}\) g, option (A). \[ \boxed{\text{(A)}} \]