Question

a. what effect does adding a solute to a solvent have on the freezing point of the solvent? what equation describes the effect? (1 point)
b. what effect does adding a solute to a solvent have on the boiling point of the solvent? what equation describes the effect? (1 point)
question 6: the ideal gas law (7 points)
a. what is the mathematical equation for the ideal gas law? identify each variable and give its units. (2 points)

Explanation:

a. Freezing - point depression

Adding a solute to a solvent lowers the freezing - point of the solvent. This is called freezing - point depression. The equation is $\Delta T_f = iK_fm$, where $\Delta T_f$ is the change in freezing - point (in $^{\circ}C$ or $K$), $i$ is the van't Hoff factor (unitless), $K_f$ is the cryoscopic constant of the solvent (in $^{\circ}C/m$ or $K/m$), and $m$ is the molality of the solution (in $mol/kg$).

b. Boiling - point elevation

Adding a solute to a solvent raises the boiling - point of the solvent. This is called boiling - point elevation. The equation is $\Delta T_b = iK_bm$, where $\Delta T_b$ is the change in boiling - point (in $^{\circ}C$ or $K$), $i$ is the van't Hoff factor (unitless), $K_b$ is the ebullioscopic constant of the solvent (in $^{\circ}C/m$ or $K/m$), and $m$ is the molality of the solution (in $mol/kg$).

c. Ideal gas law

The mathematical equation for the ideal gas law is $PV = nRT$. Here, $P$ is the pressure of the gas (units: $Pa$, $atm$, $mmHg$, etc.), $V$ is the volume of the gas (units: $m^3$, $L$, etc.), $n$ is the number of moles of the gas (units: $mol$), $R$ is the ideal gas constant ($R = 8.314\ J/(mol\cdot K)$ when $P$ is in $Pa$ and $V$ is in $m^3$, $R= 0.0821\ L\cdot atm/(mol\cdot K)$ when $P$ is in $atm$ and $V$ is in $L$), and $T$ is the temperature of the gas (units: $K$).

Answer:

a. Adding a solute lowers the freezing - point. Equation: $\Delta T_f = iK_fm$.
b. Adding a solute raises the boiling - point. Equation: $\Delta T_b = iK_bm$.
c. Equation: $PV = nRT$. $P$: pressure (varies), $V$: volume (varies), $n$: moles ($mol$), $R$: ideal gas constant (varies by units), $T$: temperature ($K$).