Respuesta :
The compound involved is copper(II) sulfate pentahydrate, that is, CuSO₄.5H₂O.
The heat will make the water separate, so the balanced equation is:
[tex]CuSO_4.5H_2O(s)\to CuSO_4(s)+5H_2O(g)[/tex]Since we start with one compound and end with more than on, this is a decomposition reaction.
Since we started with 8.924 g of CuSO₄.5H₂O, we can calculate how many moles are there to make the stoichiometry of the products.
The equation we use for transforming mass to number of moles or the other way around is:
[tex]M=\frac{m}{n}_{}[/tex]Where M is the molar weight of the compound.
The molar weight of CuSO₄.5H₂O is:
[tex]\begin{gathered} M_{CuSO_4.5H_2O}=1\cdot M_{Cu}+1\cdot M_S+9\cdot M_O+10\cdot M_H \\ M_{CuSO_4.5H_2O}=(1\cdot63.546+1\cdot32.065+9\cdot15.9994+10\cdot1.00794)g/mol \\ M_{CuSO_4.5H_2O}=(63.546+32.065+143.9946+10.0794)g/mol \\ M_{CuSO_4.5H_2O}=249.6850g/mol \end{gathered}[/tex]Thus, the number of moles is:
[tex]\begin{gathered} M_{CuSO_{4}.5H_{2}O}=\frac{m_{CuSO_4.5H_2O}}{n_{CuSO_{4}.5H_{2}O}} \\ n_{CuSO_4.5H_2O}=\frac{m_{CuSO_4.5H_2O}}{M_{CuSO_{4}.5H_{2}O}}=\frac{8.924g}{249.6850g/mol}=0.035741\ldots mol \end{gathered}[/tex]The reaction is 1 to 1 for CuSO₄ and 1 to 5 for H₂O, so this reaction will produce:
[tex]\begin{gathered} n_{CuSO_4}=\frac{1}{1}n_{CuSO_4.5H_2O}=0.035741\ldots mol \\ n_{H_2O}=\frac{5}{1}n_{CuSO_4.5H_2O}=5\cdot0.035741mol=_{}0.17870\ldots mol \end{gathered}[/tex]Now, we just need to convert these to mass, but first we need the molar weight of CuSO₄ and H₂O:
[tex]\begin{gathered} M_{CuSO_4}=1\cdot M_{Cu}+1\cdot M_S+4\cdot M_O \\ M_{CuSO_4}=(1\cdot63.546+1\cdot32.065+4\cdot15.9994)g/mol \\ M_{CuSO_4}=(63.546+32.065+63.9976)g/mol \\ M_{CuSO_4}=159.6086g/mol \end{gathered}[/tex][tex]\begin{gathered} M_{H_2O}=2\cdot M_H+1\cdot M_O \\ M_{H_2O}=(2\cdot1.00794+1\cdot15.9994)g/mol \\ M_{H_2O}=(2.01588+15.9994)g/mol \\ M_{H_2O}=18.01528g/mol \end{gathered}[/tex]So, we have:
[tex]\begin{gathered} M_{CuSO_4}=\frac{m_{CuSO_4}}{n_{CuSO_{4}}} \\ m_{CuSO_4}=n_{CuSO_4}\cdot M_{CuSO_4}=0.035741\ldots mol\cdot159.6086g/mol\approx5.705g \end{gathered}[/tex][tex]\begin{gathered} M_{H_{2}O}=\frac{m_{H_2O}}{n_{H_{2}O}} \\ m_{H_2O}=n_{H_2O}\cdot M_{H_2O}=0.17870\ldots mol\cdot18.01528g/mol\approx3.219g \end{gathered}[/tex]So, in the end we will have 0 g of copper(II) sulfate pentahydrate, approximately 5.705 g of copper(II) sulfate and approximately 3.219 g of water.