Answer to Question #95172 in General Chemistry for josh

Question #95172
5.17 grams of CaCl 2 was added to 85.0 cm 3 of water in a Styrofoam cup calorimeter. The temperature of the water changed from 21.4°C to 27.5 °C.
Calculate the molar q value (q mol) for dissolving 5.17 grams of CaCl 2 in 85.0 cm 3 of water.
Assume the heat capacity of the system is due only to the water in the system. The specific heat of water is 4.18 J/(g∙°C).
1
Expert's answer
2019-09-24T05:57:50-0400

The amout of heat needed to change the temperature of water can be calculated as


"Q = c{m_{{H_2}O}}\\Delta T"


where "{m_{{H_2}O}} = \\rho V" - the mass of water and "c" is the specific heat of water. Now let's fint "Q"


"Q = c\\rho V\\Delta T = 4180[\\frac{{\\rm{J}}}{{{\\rm{kg}} \\cdot {\\rm{^\\circ C}}}}] \\cdot 1000[\\frac{{{\\rm{kg}}}}{{{{\\rm{m}}^{\\rm{3}}}}}] \\cdot 85.0 \\cdot {10^{ - 6}}[{{\\rm{m}}^3}] \\cdot (27.5[{\\rm{^\\circ C}}] - 21.4[{\\rm{^\\circ C}}]) = 2167.33[{\\rm{J}}]"

(we use that "V = 85.0[{\\rm{c}}{{\\rm{m}}^3}] = 85.0 \\cdot {10^{ - 6}}[{{\\rm{m}}^3}]" and "c = 4.18[\\frac{{\\rm{J}}}{{{\\rm{g}} \\cdot {\\rm{^\\circ C}}}}] = 4180[\\frac{{\\rm{J}}}{{{\\rm{kg}} \\cdot {\\rm{^\\circ C}}}}]" )

Next we can find the number of moles in "5.17[{\\rm{g}}]" grams of "CaC{l_2}" . Calculate the molar mass of "CaC{l_2}"

"{M_{CaC{l_2}}} = {M_{Ca}} + 2{M_{Cl}} = 40.08[\\frac{{\\rm{g}}}{{{\\rm{mol}}}}] + 2 \\cdot 35.45[\\frac{{\\rm{g}}}{{{\\rm{mol}}}}] = 110.98[\\frac{{\\rm{g}}}{{{\\rm{mol}}}}]"

(atomic weights of atoms can be found in the periodic table). Thus the number of moles is


"\\nu = \\frac{m}{{{M_{CaC{l_2}}}}} = \\frac{{5.17[{\\rm{g}}]}}{{110.98[\\frac{{\\rm{g}}}{{{\\rm{mol}}}}]}} \\approx 0.047[{\\rm{mol}}]"

and the molar heat of solution is


"{C_\\nu } = \\frac{Q}{\\nu } = \\frac{{2167.33[{\\rm{J}}]}}{{0.047[{\\rm{mol}}]}} \\approx 46113.4[\\frac{{\\rm{J}}}{{{\\rm{mol}}}}]"

(!!!)Note: please check the initial conditions of the problem - they can be wrong because the real value is "{C_\\nu } \\approx 83000[\\frac{{\\rm{J}}}{{{\\rm{mol}}}}]" )



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