Respuesta :
Answer:
[tex]P_{sol}=50.4\ mm.Hg[/tex]
Explanation:
According to given:
- molecular mass of glycerin, [tex]M_g=3\times 12+8+3\times 16=92\ g.mol^{-1}[/tex]
- molecular mass of water, [tex]M_w=2+16=18\ g.mol^{-1}[/tex]
- ∵Density of water is [tex]0.992\ g.cm^{-3}= 0.992\ g.mL^{-1}[/tex]
- ∴mass of water in 316 mL, [tex]m_w=316\times 0.992=313.5 g[/tex]
- mass of glycerin, [tex]m_g=154\ g[/tex]
- pressure of mixture, [tex]P_x=55.32\ torr= 55.32\ mm.Hg[/tex]
- temperature of mixture, [tex]T_x=40^{\circ}C[/tex]
Upon the formation of solution the vapour pressure will be reduced since we have one component of solution as non-volatile.
moles of water in the given quantity:
[tex]n_w=\frac{m_w}{M_w}[/tex]
[tex]n_w=\frac{313.5}{18}[/tex]
[tex]n_w=17.42 moles[/tex]
moles of glycerin in the given quantity:
[tex]n_g=\frac{m_g}{M_g}[/tex]
[tex]n_g=\frac{154}{92}[/tex]
[tex]n_g=1.674 moles[/tex]
Now the mole fraction of water:
[tex]X_w=\frac{n_w}{n_w+n_g}[/tex]
[tex]X_w=\frac{17.42}{17.42+1.674}[/tex]
[tex]X_w=0.912[/tex]
Since glycerin is non-volatile in nature so the vapor pressure of the resulting solution will be due to water only.
[tex]\therefore P_{sol}=X_w\times P_x[/tex]
[tex]\therefore P_{sol}=0.912\times 55.32[/tex]
[tex]P_{sol}=50.4\ mm.Hg[/tex]
