Question

balance the chemical equation below using the smallest possible whole number stoichiometric coefficients. 2c(s) + h₂(g) → c₂h₆(g)

Explanation:

Step1: Balance Carbon atoms

On the left, we have 2 C atoms (from \(2C(s)\)). On the right, in \(C_2H_6(g)\), we also have 2 C atoms. So C is balanced for now.

Step2: Balance Hydrogen atoms

On the left, from \(H_2(g)\), we have 2 H atoms. On the right, in \(C_2H_6(g)\), we have 6 H atoms. To balance H, we need to find a coefficient for \(H_2(g)\) such that the number of H atoms on the left equals 6. Let the coefficient of \(H_2(g)\) be \(x\). Then \(2x = 6\), so \(x = 3\).

Now, check the C atoms again. Wait, no, the left C is 2 (from \(2C(s)\)) and right C is 2 (from \(C_2H_6(g)\)), so C is still balanced. Wait, no, wait the original equation was \(2C(s)+H_2(g)
ightarrow C_2H_6(g)\). After balancing H, we need to put 3 in front of \(H_2(g)\). But wait, let's re - write:

The unbalanced equation: \(C(s)+H_2(g)
ightarrow C_2H_6(g)\) (Wait, maybe a typo in the original, maybe it's \(C(s)\) not \(2C(s)\) initially? Wait, the user provided \(2C(s)+H_2(g)
ightarrow C_2H_6(g)\). Let's check again.

Left C: 2, Right C: 2 (in \(C_2H_6\)). Left H: 2 (from \(H_2\)), Right H: 6 (from \(C_2H_6\)). So to balance H, we need 3 moles of \(H_2\) (since \(3\times2 = 6\) H atoms). But the left C is 2, right C is 2, so C is balanced. Wait, but the original equation has \(2C(s)\), so let's correct:

Wait, maybe the original equation was supposed to be \(C(s)+H_2(g)
ightarrow C_2H_6(g)\), but the user wrote \(2C(s)\). Wait, no, let's do it properly.

Let's start over.

Let the balanced equation be \(aC(s)+bH_2(g)
ightarrow cC_2H_6(g)\)

For C: \(a = 2c\)

For H: \(2b=6c\Rightarrow b = 3c\)

We want the smallest whole numbers, so let \(c = 1\). Then \(a = 2\), \(b = 3\)

So the balanced equation is \(2C(s)+3H_2(g)
ightarrow C_2H_6(g)\)

Wait, but the original left side had \(2C(s)\) and \(H_2(g)\), so we need to put 3 in front of \(H_2(g)\)

Answer:

The balanced equation is \(\boldsymbol{2C(s)+3H_2(g)
ightarrow C_2H_6(g)}\)