A) \[\Delta {{T}_{f}}=\frac{{{(273)}^{2}}\times 1.5}{{{(373)}^{2}}}\]
B) \[\Delta {{T}_{f}}=\frac{{{(273)}^{2}}\times 0.5}{{{(373)}^{2}}}\]
C) \[\Delta {{T}_{f}}=\frac{{{(373)}^{2}}\times 1.5}{{{(273)}^{2}}}\]
D) \[\Delta {{T}_{f}}=\frac{{{(373)}^{2}}\times 0.5}{{{(273)}^{2}}}\]
Correct Answer: A
Solution :
[a] \[\Delta {{T}_{b}}={{K}_{b}}\times m\] \[\Delta {{T}_{f}}={{K}_{f}}\times m\] \[\frac{\Delta {{T}_{f}}}{\Delta {{T}_{b}}}\frac{{{K}_{f}}}{{{K}_{b}}}\] \[=\frac{RT_{2}^{f}}{RT_{b}^{2}}\frac{1000{{l}_{v}}}{1000{{l}_{f}}}\] \[=\frac{T_{f}^{2}}{T_{b}^{2}}\frac{{{l}_{v}}}{{{l}_{f}}}\] \[{{T}_{b}}=100+273=373K\] \[{{T}_{f}}=273K\] \[\Delta {{T}_{b}}=100.3-100=0.3{}^\circ C\] \[\frac{\Delta {{T}_{f}}}{0.3}=\frac{{{(272)}^{2}}}{{{(373)}^{2}}}\times \frac{500}{100}\] \[\Delta {{T}_{f}}=\frac{{{(273)}^{2}}\times 1.5}{{{(373)}^{2}}}\]
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