Which of the following weighs the most?

Options

A. `10^23` molecules of `H_2`
B. 1 mole of `H_2O`
C. 1 mole of `N_2`
D. `10^22` atoms of oxygen

Explanation

To determine which of the given substances weighs the most, we will calculate the weight of each substance based on the number of molecules provided. Let's break down the solution step by step.

### Step 1: Understand the Molar Masses
- **Hydrogen (H2)**: The molar mass of H2 is 2 g/mol.
- **Water (H2O)**: The molar mass of H2O is 18 g/mol.
- **Nitrogen (N2)**: The molar mass of N2 is 28 g/mol.
- **Oxygen (O2)**: The molar mass of O2 is 32 g/mol.

### Step 2: Calculate the Weight of 23 Molecules of H2
1. Use Avogadro's number (6.022 x 10^23) to find the weight of 23 molecules of H2.
2. The weight of 1 mole (6.022 x 10^23 molecules) of H2 is 2 g.
3. Therefore, the weight of 23 molecules of H2 can be calculated as follows:

\[ \text{Weight of 23 molecules of H2} = \frac{23}{6.022 \times 10^{23}} \times 2 \text{ g} \approx 0.33 \text{ mg} \]

### Step 3: Calculate the Weight of 23 Molecules of H2O
1. The weight of 1 mole of H2O is 18 g.
2. Therefore, the weight of 23 molecules of H2O can be calculated similarly:

\[ \text{Weight of 23 molecules of H2O} = \frac{23}{6.022 \times 10^{23}} \times 18 \text{ g} \approx 0.68 \text{ mg} \]

### Step 4: Calculate the Weight of 23 Molecules of N2
1. The weight of 1 mole of N2 is 28 g.
2. Therefore, the weight of 23 molecules of N2 can be calculated as follows:

\[ \text{Weight of 23 molecules of N2} = \frac{23}{6.022 \times 10^{23}} \times 28 \text{ g} \approx 1.06 \text{ mg} \]

### Step 5: Calculate the Weight of 23 Molecules of O2
1. The weight of 1 mole of O2 is 32 g.
2. Therefore, the weight of 23 molecules of O2 can be calculated as follows:

\[ \text{Weight of 23 molecules of O2} = \frac{23}{6.022 \times 10^{23}} \times 32 \text{ g} \approx 1.15 \text{ mg} \]

### Step 6: Compare the Weights
Now we can summarize the weights calculated:
- Weight of 23 molecules of H2: 0.33 mg
- Weight of 23 molecules of H2O: 0.68 mg
- Weight of 23 molecules of N2: 1.06 mg
- Weight of 23 molecules of O2: 1.15 mg

### Conclusion
Among the substances calculated, the one that weighs the most is **O2** (oxygen), with a weight of approximately 1.15 mg.