Answer:
2.0978 g/cm^3
Explanation:
Given data:
[tex]p=1.91 g/cm^{3}[/tex]
w = 9.5 %
[tex]G_{s}[/tex]= 2.70
e =?
[tex]S_{r}[/tex] =?
solution:
[tex]w=\frac{mass of water}{mass of solid} =\frac{m_{w} }{m_{s} }[/tex]
[tex]e=\frac{volume of solid}{volume of solid} =\frac{V_{s} }{V_{s} }[/tex]
assume total volume [tex]V_{total}[/tex]=1 [tex]cm^{3}[/tex]=[tex]V_{w} +V_{s} +V_{air}[/tex]
[tex]p=\frac{m_{total} }{V_{total} }[/tex]
[tex]m_{total} =1.91 g\\m_{total} =m_{w} +m_{s}\\w=\frac{m_{w} }{m_{s}}\\ 0.095.m_{s}=m_{w}\\1.91=m_{s}+0.095.m_{s}\\m_{s}=1.744 g\\m_{w}=0.166 g\\[/tex]
[tex]p_{w} =\frac{m_{w} }{V_{w} } ==> V\\G_{S}=\frac{m_{s} }{V_{s}.p_{w}}\\2.70=\frac{1.744}{V_{s}.1 } \\\V_{s}=0.646 cm^{3} \\V_{v}=V_{T}-V_{S}=0.354 cm^{3} \\e=\frac{V_{v}}{V_{S}} =\frac{0.354}{0.646}=0.55=55 percent\\[/tex]
[tex]S_{r}=\frac{w*Gs}{e} =0.4666=46.6 percent\\if S_{r}=1 \\ w=??\\S_{r}=\frac{w*Gs}{e} \\\\w=0.204=20.4 percent\\[/tex]
now find [tex]p[/tex]
[tex]p=\frac{m_{t}(=m_{w} +m_{s} )}{V_{t} }[/tex]
[tex]p[/tex]=2.0978 g/cm^3
