A solution of $6.85 \mathrm{~g}$ of a carbohydrate in $100.0 \mathrm{~g}$ of water has a density of $1.024 \mathrm{~g} / \mathrm{mL}$ and an osmotic pressure of $4.61 \mathrm{~atm}$ at $20.0^{\circ} \mathrm{C}$. Calculate the molar mass of the carbohydrate.

A sample of nitrogen gas expands in volume from 1.6 to 5.4 L at constant temperature. Calculate the work done in joules if the gas expands (a) against a vacuum, (b) against a constant pressure of 0.80 atm, and (c) against a constant pressure of 3.7 atm. $\left(1\;\mathrm{L\cdot atm}=101.3\;\mathrm{J}\right)$

A solution of 6.85 g of a carbohydrate in 100.0 g of water has a density of 1.024 $\mathrm{~g} / \mathrm{mL}$ and an osmotic pressure of 4.61 atm at $20.0^{\circ} \mathrm{C}$. Calculate the molar mass of the carbohydrate.

How would you prepare the following aqueous solutions? 2.5 L of 0.65 M NaCl from solid NaCl

At 850 °C, $\mathrm{CaCO_3}$ undergoes substantial decomposition to yield $\mathrm{CaO}$ and $\mathrm{CO_2}$. Assuming that the $\Delta H_f°$ values of the reactant and products are the same at 850 °C as they are at 25 °C, calculate the enthalpy change (in kJ) if 66.8 g of $\mathrm{CO_2}$ is produced in one reaction.

A quantity of $7.480 \mathrm{~g}$ of an organic compound is dissolved in water to make $300.0 \mathrm{~mL}$ of solution. The solution has an osmotic pressure of $1.43$ atm at $27^{\circ} \mathrm{C}$. The analysis of this compound shows that it contains $41.8$ percent $\mathrm{C}$, $4.7$ percent $\mathrm{H}, 37.3$ percent $\mathrm{O}$, and $16.3$ percent $\mathrm{N}$. Calculate the molecular formula of the compound.

Crystalline silicon has a cubic structure. The unit cell edge length is $543 \mathrm{pm}$. The density of the solid is $2.33 \mathrm{~g} / \mathrm{cm}^3$. Calculate the number of Si atoms in one unit cell.

A solution containing $0.8330 \mathrm{~g}$ of a polymer of unknown structure in $170.0 \mathrm{~mL}$ of an organic solvent was found to have an osmotic pressure of $5.20 \mathrm{mmHg}$ at $25^{\circ} \mathrm{C}$. Determine the molar mass of the polymer.

Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and 1.0*10^(-3) atm, respectively. How many ozone molecules are present in 1.0 L of air under these conditions?

Five males with an​ X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the​ X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied. x: 0, 1, 2, 3, 4, 5 P(x): 0.027, 0.162, 0.311, 0.311, 0.162, 0.027

The molar mass of benzoic acid $\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{COOH}\right)$ determined by measuring the freezing-point depression in benzene is twice what we would expect for the molecular formula, $\mathrm{C}_7 \mathrm{H}_6 \mathrm{O}_2$. Explain this apparent anomaly.

Molecular chlorine and molecular fluorine combine to form a gaseous product. Under the same conditions of temperature and pressure it is found that one volume of Cl2 reacts with three volumes of F2 to yield two volumes of the product. What is the formula of the product?

A solution of $2.50 \mathrm{~g}$ of a compound having the empirical formula $\mathrm{C}_6 \mathrm{H}_5 \mathrm{P}$ in $25.0 \mathrm{~g}$ of benzene is observed to freeze at $4.3^{\circ} \mathrm{C}$. Calculate the molar mass of the solute and its molecular formula.

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives, inks, and pharmaceuticals) showed that it contained $40.0$ percent $\mathrm{C}, 6.7$ percent $\mathrm{H}$, and $53.3$ percent $\mathrm{O}$. A solution of $0.650 \mathrm{~g}$ of the solid in $27.8 \mathrm{~g}$ of the solvent diphenyl gave a freezing-point depression of $1.56^{\circ} \mathrm{C}$. Calculate the molar mass and molecular formula of the solid. ( $K_{\mathrm{f}}$ for diphenyl is $8.00^{\circ} \mathrm{C} / \mathrm{m}$.)