Calculate the standard enthalpy change of following reaction. aligned & CH _ 4( ~g ) +2 O _ 2( ~g ) CO _ 2( ~g ) +2 H ₂ O _ ( ) & if _ f H ^ (C H₄ )=-75 ~kJ ~mol ⁻¹ & _ f H ^ (C O ₂ )=-390 ~kJ ~mol ⁻¹ & _ f H ^ ( H ₂ O )=-286 ~kJ ~mol ⁻¹ aligned

Step-by-step solution

The standard enthalpy change of the reaction is calculated using the formula: _ r H ^ = n _ f H ^ ( products ) - m _ f H ^ ( reactants ) For the reaction CH _ 4( g ) + 2 O _ 2( g ) CO _ 2( g ) + 2 H ₂ O _ ( ) with given enthalpies: _ f H ^ ( CH ₄) = -75 kJ mol⁻¹ , _ f H ^ ( CO ₂) = -390 kJ mol⁻¹ , _ f H ^ ( H ₂ O ) = -286 kJ mol⁻¹ , and noting _ f H ^ ( O ₂) = 0 kJ mol⁻¹ : _ r H ^ = [1 (-390) + 2 (-286)] - [1 (-75) + 2 0] = [-390 - 572] - [-75] = -962 + 75 = -887 kJ The standard enthalpy change of the reaction is -