Question

The mass of hydrogen in grams present in \(1.0\ \text{L}\) of pure water of density \(1.0\ \text{g cm}^{-3}\) is:

• A. \(1.11\times10^2\)
• B. \(5.55\times10^2\)
• C. \(2.22\times10^2\)
• D. \(3.33\times10^2\)

Hint:

In water, the mass fraction of hydrogen is: \[ \frac{2}{18}=\frac{1}{9} \] So, mass of hydrogen can be found by multiplying the mass of water by \(\frac{1}{9}\).

Answer 1

The Correct Option is A

Step 1: Find the mass of 1.0 L of pure water.
Given density of water = 1.0 g/cm3 and volume = 1.0 L = 1000 cm3: \[ \text{mass of water} = 1000\ \text{cm}^3 \times 1.0\ \text{g/cm}^3 = 1000\ \text{g} \]

Step 2: Recall the molar mass of water.
Water is H2O. Molar mass = \(2(1) + 16 = 18\) g/mol.
In each molecule of water, hydrogen contributes a mass of \(2 \times 1 = 2\) g per 18 g of water.

Step 3: Calculate the mass fraction of hydrogen in water.
\[ \text{mass fraction of H} = \frac{2}{18} = \frac{1}{9} \]
This means for every 9 grams of water, 1 gram is hydrogen.

Step 4: Calculate the total mass of hydrogen in 1000 g of water.
\[ \text{mass of H} = 1000 \times \frac{1}{9} = \frac{1000}{9} \approx 111.1\ \text{g} \]

Step 5: Express the answer in scientific notation.
\[ 111.1\ \text{g} \approx 1.11 \times 10^2\ \text{g} \]

Step 6: State the final answer.
The mass of hydrogen present in 1.0 L of pure water is approximately \(1.11 \times 10^2\) grams. Note that hydrogen makes up about 11.1% by mass of water, consistent with our calculation.
\[ \boxed{1.11 \times 10^2\ \text{g}} \]