$5\mathrm{.}3$ The equilibrium partial pressure of water vapor in contact with a certain silica gel on which

water is adsorbed is$,$ at $25C,$ as follows:

$($a$)$ Plot the equilibrium data as $\frac{?}{\text{b}\text{a}\text{r}}(p)=$ partial pressure of water vapor against $x=$ wt fraction

water in the gel.

$($b$)$ Plot the equilibrium data as $x=$mol water $\frac{?}{\text{m}\text{a}\text{s}\text{s}}$ dry gel, $Y=$mol water vapor $\frac{?}{\text{m}\text{o}\text{l}\text{d}\text{r}\text{y}}$

air, for a total pressure of $1std$ atm.

$($c$)$ When $10lb(4\mathrm{.}54kg)$ of silica gel containing $5wt\%$ adsorbed water is placed in a flowing

airstream containing a partial pressure of water vapor $=12mmHg,$ the total pressure is $1std$ atm

and the temperature $25C.$ When equilibrium is reached, what mass of additional water will the gel

have adsorbed? Air is not adsorbed.

$($d$)$ One pound mass $(0\mathrm{.}454kg)$ of silica gel containing $5wt\%$ adsorbed water is placed in a

vessel in which there are $400f{t}^3(11\mathrm{.}33m^3)$ moist air whose partial pressure of water is $15mmHg.$

The total pressure and temperature are kept at $1std$ atm and $25C,$ respectively. At equilibrium,

what will be the moisture content of the air and gel and the mass of water adsorbed by the gel? Ans.:

$0\mathrm{.}0605kg$ water.

$($e$)$ Write the equation of the operating line for part $($d$)$ in terms of $x$ and $Y.$ Convert this into

an equation in terms of $\frac{?}{\text{b}\text{a}\text{r}}(p)$ and $x,$ and plot the operating curve on $\frac{?}{\text{b}\text{a}\text{r}}(p),x$ coordinates.

$(f)$ If $1lb(0\mathrm{.}454kg)$ of silica gel containing $18\%$ adsorbed water is placed in a vessel containing

$500f{t}^3(14\mathrm{.}16m^3)$ dry air and the temperature and pressure are maintained at $25C$ and $1$stdatm,

respectively, what will be the final equilibrium moisture content of the air and the gel.

$(g)$ Repeat part $(f)$ for a total pressure of $2std$ atm. Note that the equilibrium curve in terms of

$x$ and $Y$ previously used is not applicable.