Question

Calculate the enthalpy of solution (in kJ/mol) for dissolving 10.0 g of NaOH(s) in 100.0 g of water at 25°C, given that the final temperature of the solution is 28.5°C and the heat capacity of the solution is 4.18 J/g°C.

Answer 1

To calculate the enthalpy of solution, we first need to find the heat  q  released or absorbed during the dissolving process. We can use the formula:q = mcTwhere m is the mass of the solution  in grams , c is the heat capacity of the solution  in J/gC , and T is the change in temperature  in C .First, let's find the mass of the solution. We are given the mass of NaOH  10.0 g  and the mass of water  100.0 g . The mass of the solution is the sum of these two masses:m_solution = m_NaOH + m_waterm_solution = 10.0 g + 100.0 gm_solution = 110.0 gNext, we need to find the change in temperature. We are given the initial temperature  25C  and the final temperature  28.5C . The change in temperature is:T = T_final - T_initialT = 28.5C - 25CT = 3.5CNow we can find the heat  q  released or absorbed during the dissolving process:q = mcTq =  110.0 g  4.18 J/gC  3.5C q = 1610.3 JSince the temperature of the solution increased, the dissolving process is exothermic, and the heat is released. Therefore, q = -1610.3 J.Now we need to find the enthalpy of solution  H_solution  in kJ/mol. We can use the formula:H_solution = q / nwhere n is the number of moles of NaOH.First, let's find the number of moles of NaOH. The molar mass of NaOH is:M_NaOH = 22.99 g/mol  Na  + 15.999 g/mol  O  + 1.007 g/mol  H M_NaOH = 39.996 g/molNow we can find the number of moles of NaOH:n = mass / molar_massn = 10.0 g / 39.996 g/moln = 0.250 molNow we can find the enthalpy of solution:H_solution = q / nH_solution = -1610.3 J / 0.250 molH_solution = -6441.2 J/molSince we need the answer in kJ/mol, we can convert it:H_solution = -6.441 kJ/molTherefore, the enthalpy of solution for dissolving 10.0 g of NaOH in 100.0 g of water at 25C is -6.441 kJ/mol.