Solve 6.0gC*1molC/12.0gC=0.50molC

$$6.0 g C \times \frac { 1 mol C } { 12.0 g C } = 0.50 mol C$$

Solve for C

$$C\neq 0$$

Solution Steps

Variable C cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12Cg.

$$6gC\times 1molC=0.5molC\times 12Cg$$

Multiply 6 and 1 to get 6.

$$6gCmolC=0.5molC\times 12Cg$$

Multiply C and C to get C^{2}.

$$6gC^{2}mol=0.5molC\times 12Cg$$

Multiply C and C to get C^{2}.

$$6gC^{2}mol=0.5molC^{2}\times 12g$$

Multiply 0.5 and 12 to get 6.

$$6gC^{2}mol=6molC^{2}g$$

Subtract 6molC^{2}g from both sides.

$$6gC^{2}mol-6molC^{2}g=0$$

Combine 6gC^{2}mol and -6molC^{2}g to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any C.

$$C\in \mathrm{R}$$

Variable C cannot be equal to 0.

$$C\in \mathrm{R}\setminus 0$$

Solve for g

$$g\neq 0$$

Solution Steps

Variable g cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12Cg.

$$6gC\times 1molC=0.5molC\times 12Cg$$

Multiply 6 and 1 to get 6.

$$6gCmolC=0.5molC\times 12Cg$$

Multiply C and C to get C^{2}.

$$6gC^{2}mol=0.5molC\times 12Cg$$

Multiply C and C to get C^{2}.

$$6gC^{2}mol=0.5molC^{2}\times 12g$$

Multiply 0.5 and 12 to get 6.

$$6gC^{2}mol=6molC^{2}g$$

Subtract 6molC^{2}g from both sides.

$$6gC^{2}mol-6molC^{2}g=0$$

Combine 6gC^{2}mol and -6molC^{2}g to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any g.

$$g\in \mathrm{R}$$

Variable g cannot be equal to 0.

$$g\in \mathrm{R}\setminus 0$$