Do the coefficients in a balanced chemical equation represent volume ratios for solids and liquids? explain.

No, The coefficients in a balanced chemical equation do not represent volume ratios for solids and liquids.

Explanation:
                   The coefficients in equation are only applicable for gases particularly Ideal Gases. This is because in Ideal gases there is zero interaction between the particles and particles are apart (approximately 1000 times that of Liquids and Solids) from each other. 
                    In case of Liquids and Solids the particles are very close to each other, So, the molar volume of Solids and Liquids will contain a large number of particles as compare to Molar volumes of Ideal gases (i.e 22.4 dm³ for 1 mole) at standard Temperature and Pressure.