In the reaction,
`CO(g)+2H_2(g) rarr CH_3OH(g)`
How many molecules of `H_2` would be needed in consume 2 mol of CO?

Options

A. 4 molecules
B. 2 molecules
C. `12 xx 10^(-1)` molecules
D. `2.4 xx 10^24` molecules

Answer

To solve the problem, we need to determine how many molecules of \( H_2 \) are required to consume 2 moles of \( CO \) in the reaction:

\[ CO(g) + 2H_2(g) \rightarrow CH_3OH(g) \]

### Step-by-step Solution:

1. **Understand the Reaction Stoichiometry**:
From the balanced chemical equation, we see that 1 mole of \( CO \) reacts with 2 moles of \( H_2 \).

2. **Calculate Moles of \( H_2 \) Needed for 2 Moles of \( CO \)**:
If 1 mole of \( CO \) requires 2 moles of \( H_2 \), then for 2 moles of \( CO \):
\[ \text{Moles of } H_2 = 2 \text{ moles of } H_2 \times 2 \text{ moles of } CO = 4 \text{ moles of } H_2 \]

3. **Convert Moles of \( H_2 \) to Molecules**:
To find the number of molecules, we use Avogadro's number, which states that 1 mole of any substance contains \( 6.022 \times 10^{23} \) molecules.
\[ \text{Molecules of } H_2 = 4 \text{ moles of } H_2 \times 6.022 \times 10^{23} \text{ molecules/mole} \]

4. **Perform the Calculation**:
\[ \text{Molecules of } H_2 = 4 \times 6.022 \times 10^{23} = 24.088 \times 10^{23} \text{ molecules} \]

5. **Express in Scientific Notation**:
We can express \( 24.088 \times 10^{23} \) in scientific notation:
\[ 24.088 \times 10^{23} = 2.4088 \times 10^{24} \text{ molecules} \]
Rounding to one decimal place gives:
\[ \approx 2.4 \times 10^{24} \text{ molecules} \]

### Final Answer:
Thus, the number of molecules of \( H_2 \) needed to consume 2 moles of \( CO \) is approximately \( 2.4 \times 10^{24} \) molecules.