Answer:- 544.5 mL of water need to be added.
Solution:- It is a dilution problem. The equation used for solving this type of problems is:
![M_1V_1=M_2V_2](https://tex.z-dn.net/?f=M_1V_1%3DM_2V_2)
where,
is initial molarity and
is the molarity after dilution. Similarly,
is the volume before dilution and
is the volume after dilution.
Let's plug in the values in the equation:
![1.25M(363mL)=0.50M(V_2)](https://tex.z-dn.net/?f=1.25M%28363mL%29%3D0.50M%28V_2%29)
![V_2=\frac{1.25M(363mL)}{0.50M}](https://tex.z-dn.net/?f=V_2%3D%5Cfrac%7B1.25M%28363mL%29%7D%7B0.50M%7D)
![V_2=907.5mL](https://tex.z-dn.net/?f=V_2%3D907.5mL)
Volume of water added = 907.5mL - 363mL = 544.5 mL
So, 544.5 mL of water are need to be added to the original solution for dilution.
Answer:
1. Options A and B
2. Options B and C
3.. B. Net ∆G = -16.7 KJ/mol; C. Net ∆G = -14.2 KJ/mol
Explanation:
1. The spontaneity of a chemical reaction depends on its standard free energy change, ∆G. If ∆G is negative, the reaction is favourable, but when it is positive, the reaction is unfavorable.
Therefore, since reaction A and B have ∆G to be positive, they are unfavorable
2. Coupling an unfavorable reaction to a favourable reaction can help the reaction to proceed in the forward direction as long as the net free energy change is negative.
Coupling reaction A and C, as well as reaction B and C will make the reactions to become favourable as net ∆G is negative in both instances.
3. A and C: net ∆G = 13.8 - 30.5 = -16.7 KJ/mol
B and C: net ∆G = 16.3- 30.5 = -14.2 KJ/mol
Answer:
Concentration of dissolved salts = 34,038.76 ppm
Explanation:
Given:
Salinity of ocean water = 34
Find:
Concentration of dissolved salts
Computation:
Salinity of ocean water = 34 g/l
1g/l = 1001.14 ppm
Concentration of dissolved salts = 1001.14 ppm x 34
Concentration of dissolved salts = 34,038.76 ppm
Solution :
a). Applying the energy balance,
![$\Delta E_{sys}=E_{in}-E_{out}$](https://tex.z-dn.net/?f=%24%5CDelta%20E_%7Bsys%7D%3DE_%7Bin%7D-E_%7Bout%7D%24)
![$0=\Delta U$](https://tex.z-dn.net/?f=%240%3D%5CDelta%20U%24)
![$0=(\Delta U)_{iron} + (\Delta U)_{water}$](https://tex.z-dn.net/?f=%240%3D%28%5CDelta%20U%29_%7Biron%7D%20%2B%20%28%5CDelta%20U%29_%7Bwater%7D%24)
![$0=[mc(T_f-T_i)_{iron}] + [mc(T_f-T_i)_{water}]$](https://tex.z-dn.net/?f=%240%3D%5Bmc%28T_f-T_i%29_%7Biron%7D%5D%20%2B%20%5Bmc%28T_f-T_i%29_%7Bwater%7D%5D%24)
![$0 = 27 \times 0.45 \times (T_f - 375) + 130 \times 4.18 \times (T_f-26)$](https://tex.z-dn.net/?f=%240%20%3D%2027%20%5Ctimes%200.45%20%5Ctimes%20%28T_f%20-%20375%29%20%2B%20130%20%5Ctimes%204.18%20%5Ctimes%20%28T_f-26%29%24)
![$t_f=33.63^\circ C$](https://tex.z-dn.net/?f=%24t_f%3D33.63%5E%5Ccirc%20C%24)
b). The entropy change of iron.
![$\Delta s_{iron} = mc \ln\left(\frac{T_f}{T_i} \right)$](https://tex.z-dn.net/?f=%24%5CDelta%20s_%7Biron%7D%20%3D%20mc%20%5Cln%5Cleft%28%5Cfrac%7BT_f%7D%7BT_i%7D%20%5Cright%29%24)
![$ = 27 \times 0.45\ \ln\left(\frac{33.63 + 273}{375 + 273} \right)$](https://tex.z-dn.net/?f=%24%20%3D%2027%20%5Ctimes%200.45%5C%20%5Cln%5Cleft%28%5Cfrac%7B33.63%20%2B%20273%7D%7B375%20%2B%20273%7D%20%5Cright%29%24)
= -9.09 kJ-K
Entropy change of water :
![$\Delta s_{water} = mc \ \ln\left(\frac{T_f}{T_i} \right)$](https://tex.z-dn.net/?f=%24%5CDelta%20s_%7Bwater%7D%20%3D%20mc%20%5C%20%5Cln%5Cleft%28%5Cfrac%7BT_f%7D%7BT_i%7D%20%5Cright%29%24)
![$ = 130 \times 4.18\ \ln\left(\frac{33.63 + 273}{26 + 273} \right)$](https://tex.z-dn.net/?f=%24%20%3D%20130%20%5Ctimes%204.18%5C%20%5Cln%5Cleft%28%5Cfrac%7B33.63%20%2B%20273%7D%7B26%20%2B%20273%7D%20%5Cright%29%24)
= 10.76 kJ-K
So, the total entropy change during the process is :
![$\Delta s_{tot} = \Delta s_{iron} + \Delta s_{water} $](https://tex.z-dn.net/?f=%24%5CDelta%20s_%7Btot%7D%20%3D%20%5CDelta%20s_%7Biron%7D%20%2B%20%5CDelta%20s_%7Bwater%7D%20%24)
= -9.09 + 10.76
= 1.67 kJ-K
c). Exergy of the combined system at initial state,
![$X=(U-U_{0}) - T_0(S-S_0)+P_0(V-V_0)$](https://tex.z-dn.net/?f=%24X%3D%28U-U_%7B0%7D%29%20-%20T_0%28S-S_0%29%2BP_0%28V-V_0%29%24)
![$X=mc (T-T_0) - T_0 \ mc \ \ln \left(\frac{T}{T_0} \right)+0$](https://tex.z-dn.net/?f=%24X%3Dmc%20%28T-T_0%29%20-%20T_0%20%5C%20mc%20%5C%20%5Cln%20%5Cleft%28%5Cfrac%7BT%7D%7BT_0%7D%20%5Cright%29%2B0%24)
![$X=mc\left((T-T_0)-T_0 \ ln \left(\frac{T}{T_0} \right)\right)$](https://tex.z-dn.net/?f=%24X%3Dmc%5Cleft%28%28T-T_0%29-T_0%20%5C%20ln%20%5Cleft%28%5Cfrac%7BT%7D%7BT_0%7D%20%5Cright%29%5Cright%29%24)
![$X_{iron, i} = 27 \times 0.45\left(((375+273)-(12+273))-(12+273) \ln \frac{375+273}{12+273}\right)$](https://tex.z-dn.net/?f=%24X_%7Biron%2C%20i%7D%20%3D%2027%20%5Ctimes%200.45%5Cleft%28%28%28375%2B273%29-%2812%2B273%29%29-%2812%2B273%29%20%5Cln%20%5Cfrac%7B375%2B273%7D%7B12%2B273%7D%5Cright%29%24)
![$X_{water, i} = 130 \times 4.18\left(((26+273)-(12+273))-(12+273) \ln \frac{26+273}{12+273}\right)$](https://tex.z-dn.net/?f=%24X_%7Bwater%2C%20i%7D%20%3D%20130%20%5Ctimes%204.18%5Cleft%28%28%2826%2B273%29-%2812%2B273%29%29-%2812%2B273%29%20%5Cln%20%5Cfrac%7B26%2B273%7D%7B12%2B273%7D%5Cright%29%24)
![$X_{water, i} =-13.22 \ kJ$](https://tex.z-dn.net/?f=%24X_%7Bwater%2C%20i%7D%20%3D-13.22%20%5C%20kJ%24)
Therefore, energy of the combined system at the initial state is
![$X_{initial}=X_{iron,i} +X_{water, i}$](https://tex.z-dn.net/?f=%24X_%7Binitial%7D%3DX_%7Biron%2Ci%7D%20%2BX_%7Bwater%2C%20i%7D%24)
= 63.94 -13.22
= 50.72 kJ
Similarly, Exergy of the combined system at initial state,
![$X=(U_f-U_{0}) - T_0(S_f-S_0)+P_0(V_f-V_0)$](https://tex.z-dn.net/?f=%24X%3D%28U_f-U_%7B0%7D%29%20-%20T_0%28S_f-S_0%29%2BP_0%28V_f-V_0%29%24)
![$X=mc\left((T_f-T_0)-T_0 \ ln \left(\frac{T_f}{T_0} \right)\right)$](https://tex.z-dn.net/?f=%24X%3Dmc%5Cleft%28%28T_f-T_0%29-T_0%20%5C%20ln%20%5Cleft%28%5Cfrac%7BT_f%7D%7BT_0%7D%20%5Cright%29%5Cright%29%24)
![$X_{iron, f} = 27 \times 0.45\left(((33.63+273)-(12+273))-(12+273) \ln \frac{33.63+273}{12+273}\right)$](https://tex.z-dn.net/?f=%24X_%7Biron%2C%20f%7D%20%3D%2027%20%5Ctimes%200.45%5Cleft%28%28%2833.63%2B273%29-%2812%2B273%29%29-%2812%2B273%29%20%5Cln%20%5Cfrac%7B33.63%2B273%7D%7B12%2B273%7D%5Cright%29%24)
![$X_{water, f} = 130 \times 4.18\left(((33.63+273)-(12+273))-(12+273) \ln \frac{33.63+273}{12+273}\right)$](https://tex.z-dn.net/?f=%24X_%7Bwater%2C%20f%7D%20%3D%20130%20%5Ctimes%204.18%5Cleft%28%28%2833.63%2B273%29-%2812%2B273%29%29-%2812%2B273%29%20%5Cln%20%5Cfrac%7B33.63%2B273%7D%7B12%2B273%7D%5Cright%29%24)
![$X_{water, f} =-9677.95\ kJ$](https://tex.z-dn.net/?f=%24X_%7Bwater%2C%20f%7D%20%3D-9677.95%5C%20kJ%24)
Thus, energy or the combined system at the final state is :
![$X_{final}=X_{iron,f} +X_{water, f$](https://tex.z-dn.net/?f=%24X_%7Bfinal%7D%3DX_%7Biron%2Cf%7D%20%2BX_%7Bwater%2C%20f%24)
= 216.39 - 9677.95
= -9461.56 kJ
d). The wasted work
![$X_{in} - X_{out}-X_{destroyed} = \Delta X_{sys}$](https://tex.z-dn.net/?f=%24X_%7Bin%7D%20-%20X_%7Bout%7D-X_%7Bdestroyed%7D%20%3D%20%5CDelta%20X_%7Bsys%7D%24)
![$0-X_{destroyed} = $](https://tex.z-dn.net/?f=%240-X_%7Bdestroyed%7D%20%3D%20%24)
![$X_{destroyed} = X_{initial} - X_{final}$](https://tex.z-dn.net/?f=%24X_%7Bdestroyed%7D%20%3D%20X_%7Binitial%7D%20-%20X_%7Bfinal%7D%24)
= 50.72 + 9461.56
= 9512.22 kJ