Question

acetic acid (hc₂h₃o₂) is the primary component of vinegar. it is produced along with water (h₂o) when methanol (ch₃oh) reacts with carbon dioxide (co₂) and hydrogen gas (h₂). which chemical equation accurately represents this reaction? ch₃oh(l)+co₂(g)+h₂(g)→hc₂h₃o₂(l)+h₂o(l) ch₃oh(l)+3co₂(g)+5h₂(g)→3hc₂h₃o₂(l)+h₂o(l) 2ch₃oh(l)+2co₂(g)+h₂(g)→2hc₂h₃o₂(l)+h₂o(l) 2ch₃oh(l)+co₂(g)+2h₂(g)→2hc₂h₃o₂(l)+2h₂o(l)

Explanation:

Step1: Count atoms on both sides

For the first option:

• Carbon (C): Left side has \(1 + 1=2\) (from \(CH_3OH\) and \(CO_2\)), right side has \(2\) (from \(HC_2H_3O_2\)).
• Hydrogen (H): Left side has \(4+2 = 6\) (from \(CH_3OH\) and \(H_2\)), right side has \(4 + 2=6\) (from \(HC_2H_3O_2\) and \(H_2O\)).
• Oxygen (O): Left side has \(1+2 = 3\) (from \(CH_3OH\) and \(CO_2\)), right side has \(2+1 = 3\) (from \(HC_2H_3O_2\) and \(H_2O\)).

For the second option:

• Carbon (C): Left side has \(1+3 = 4\) (from \(CH_3OH\) and \(3CO_2\)), right side has \(3\times2=6\) (from \(3HC_2H_3O_2\)). Not balanced.

For the third option:

• Hydrogen (H): Left side has \(2\times4+2 = 10\) (from \(2CH_3OH\) and \(H_2\)), right side has \(2\times4+2 = 10\) (from \(2HC_2H_3O_2\) and \(H_2O\)).
• Oxygen (O): Left side has \(2\times1+2\times2=6\) (from \(2CH_3OH\) and \(2CO_2\)), right side has \(2\times2 + 1=5\) (from \(2HC_2H_3O_2\) and \(H_2O\)). Not balanced.

For the fourth option:

• Hydrogen (H): Left side has \(2\times4+2\times2 = 12\) (from \(2CH_3OH\) and \(2H_2\)), right side has \(2\times4+2\times2=12\) (from \(2HC_2H_3O_2\) and \(2H_2O\)).
• Oxygen (O): Left side has \(2\times1+2 = 4\) (from \(2CH_3OH\) and \(CO_2\)), right side has \(2\times2+2\times1 = 6\) (from \(2HC_2H_3O_2\) and \(2H_2O\)). Not balanced.

Answer:

\(\text{CH}_3\text{OH}_{(l)}+\text{CO}_2{(g)}+\text{H}_2{(g)}\longrightarrow\text{HC}_2\text{H}_3\text{O}_2{(l)}+\text{H}_2\text{O}_{(l)}\)