### Word equation

* ethanol + formaldehyde → water + acetone*

### Input interpretation

* CH3CH2OH + HCHO → H2O + CH3COCH3*

* Ethanol formaldehyde water acetone*

### Balanced equation

Balance the chemical equation algebraically:

* CH3CH2OH + HCHO → H2O + CH3COCH3*

Add stoichiometric coefficients, ** c1**, to the reactants and products:

* c1CH3CH2OH + c2HCHO → c3 H2O + c4 CH3COCH3*

Set the number of atoms in the reactants equal to the number of atoms in the products for ** C, H **and

*O:*C: 2c1 + c2 = 3c4

H: 6c1 + 2c = 2c3 + 6c4

O: c1 + c2 = c3 + c4

Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set ** c1 = 1** and solve the system of equations for the remaining coefficients:

* c1=1 c2=1*

* c3 = 1 c4=1*

Substitute the coefficients into the chemical reaction to obtain the balanced

equation:

**Answer**:

* CH3CH2OH + HCHO → H2O + CH3COCH3*