To determine the mole ratio of hydrogen to methane represented by the chemical equation [tex]\( C + 2H_2 \rightarrow CH_4 \)[/tex], let's analyze the balanced equation.
1. Balanced Chemical Equation: The given chemical reaction is:
[tex]\[
C + 2H_2 \rightarrow CH_4
\][/tex]
This tells us that:
- 1 mole of Carbon (C) reacts with
- 2 moles of Hydrogen gas (H_2) to form
- 1 mole of Methane (CH_4).
2. Mole Ratio: The ratio of hydrogen to methane is derived directly from the coefficients in the balanced equation:
[tex]\[
2H_2 \rightarrow 1CH_4
\][/tex]
Therefore, for every 2 moles of hydrogen gas (H_2), 1 mole of methane (CH_4) is produced.
3. Mole Ratio Calculation: To express this as a fraction:
[tex]\[
\text{Mole ratio of } H_2 \text{ to } CH_4 = \frac{2}{1} = 2
\][/tex]
So, the mole ratio of hydrogen to methane is [tex]\(2.0\)[/tex].
Therefore, the correct numerical value corresponding to the mole ratio of hydrogen to methane is:
[tex]\[
\boxed{2.0}
\][/tex]
Based on the options given in the question, the answer is not perfectly matching, but interpreted numerically, [tex]\(2.0\)[/tex] clearly indicates the correct ratio, which aligns with option 2.
