Question

Calculate the heat of mixing when 50g of ethanol (C2H5OH) is added to 200g of water initially at 25°C. Assume the density of water is 1g/mL and the specific heat capacity of water is 4.184J/(g°C). The enthalpy of vaporization of ethanol is 38.56kJ/mol and assume that ethanol-water mixture has a specific heat capacity of 4.2J/(g°C).

Answer 1

To calculate the heat of mixing, we first need to determine the final temperature of the mixture. We can do this by setting up an energy balance equation. The heat gained by the ethanol must be equal to the heat lost by the water.Let's denote the final temperature as Tf. The mass of ethanol  m_ethanol  is 50g, and the mass of water  m_water  is 200g. The specific heat capacity of the ethanol-water mixture  c_mix  is 4.2 J/ gC . The initial temperature of the water  T_water  is 25C.The energy balance equation can be written as:m_ethanol * c_mix *  Tf - T_water  = m_water * c_mix *  T_water - Tf Now we can solve for Tf:50g * 4.2 J/ gC  *  Tf - 25C  = 200g * 4.2 J/ gC  *  25C - Tf Divide both sides by 4.2 J/ gC :50g *  Tf - 25C  = 200g *  25C - Tf Now, distribute the mass on both sides:50g * Tf - 1250g = 5000g - 200g * TfCombine the terms with Tf:250g * Tf = 6250gNow, solve for Tf:Tf = 6250g / 250g = 25CSince the final temperature of the mixture is the same as the initial temperature of the water, there is no heat exchange between the ethanol and water. Therefore, the heat of mixing is 0 J.