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Calculate the standard enthalpy change for the fusion reaction of 50g of ice at 0°C with 450g of liquid water at 25°C. The molar enthalpy of fusion of ice is 6.01 kJ/mol and the specific heat capacity of water is 4.18 J/g·°C. Assume there are no heat losses to the surroundings.

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To calculate the standard enthalpy change for the fusion reaction, we need to consider the following steps:1. Melting the ice at 0C2. Heating the melted ice  now water  from 0C to the final temperature3. Cooling the liquid water from 25C to the final temperatureFirst, let's find the moles of ice and water:Molar mass of water  H2O  = 18.015 g/molMoles of ice =  50 g  /  18.015 g/mol  = 2.776 molMoles of water =  450 g  /  18.015 g/mol  = 24.986 molStep 1: Melting the ice at 0CEnthalpy change for melting ice = moles of ice  molar enthalpy of fusionH1 = 2.776 mol  6.01 kJ/mol = 16.68 kJStep 2: Heating the melted ice  now water  from 0C to the final temperatureLet Tf be the final temperature.q2 = moles of melted ice  specific heat capacity of water   Tf - 0C H2 = 2.776 mol  4.18 J/gC  18.015 g/mol   Tf - 0C Step 3: Cooling the liquid water from 25C to the final temperatureq3 = moles of water  specific heat capacity of water   Tf - 25C H3 = 24.986 mol  4.18 J/gC  18.015 g/mol   Tf - 25C Since there are no heat losses to the surroundings, the heat gained by the ice must equal the heat lost by the water:H1 + H2 = -H316.68 kJ + 2.776 mol  4.18 J/gC  18.015 g/mol   Tf - 0C  = -  24.986 mol  4.18 J/gC  18.015 g/mol   Tf - 25C  Now, we need to solve for Tf:16.68 kJ  1000 J/kJ + 2.776  4.18  18.015  Tf = 24.986  4.18  18.015   Tf - 25 16680 J + 208.58  Tf = 1874.16  Tf - 1874.16  2516680 J = 1665.58  Tf - 46854Tf =  16680 + 46854  / 1665.58Tf  32.1CNow that we have the final temperature, we can calculate the enthalpy changes for steps 2 and 3:H2 = 2.776 mol  4.18 J/gC  18.015 g/mol   32.1 - 0 H2  208.58  32.1H2  6695.5 J = 6.695 kJH3 = 24.986 mol  4.18 J/gC  18.015 g/mol   32.1 - 25 H3  1874.16  7.1H3  -13307.5 J = -13.307 kJThe standard enthalpy change for the fusion reaction is the sum of the enthalpy changes for all three steps:H = H1 + H2 + H3H = 16.68 kJ + 6.695 kJ - 13.307 kJH  10.068 kJ

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