The enthalpy of solution of nitrous oxide (N2O) in water is -12 kJ/mol and its solubility at 20 oC and 1.00 atm is 0.121 g per 100. g of water. Calculate the molal solubility of nitrous oxide in water at 1.600 atm and 20 oC. Hint, first find Henry's law constant at 20 oC and 1.00 atm.

I suppose you are to use M and m as the same.

0.121g/100 gH2O = solubility.
mol N2O = 0.121/60 = approx o.002 and 0.002/0.1kg solvent = 0.02m
p = KcC
1 atm = Kc*0.02
Kc = 1 atm/0.02 = 50 atm/m

p = KcC
1.600 = Kc from above *C
Solve for C in molality and convert to g/100 if desired.

To calculate the molal solubility of nitrous oxide (N2O) in water at 1.600 atm and 20 oC, we first need to find Henry's law constant at 20 oC and 1.00 atm.

Henry's law states that the solubility of a gas in a solvent is directly proportional to the partial pressure of the gas above the solvent. Mathematically, this can be expressed as:

C = k * P

Where C is the molal solubility of the gas, k is Henry's law constant, and P is the partial pressure of the gas.

Given that the enthalpy of solution of nitrous oxide in water is -12 kJ/mol, we can assume that the dissolution process is exothermic. This means that the solubility of nitrous oxide will increase as the temperature decreases. Therefore, we can use the given solubility at 20 oC and 1.00 atm as the basis for finding Henry's law constant.

The given solubility is 0.121 g per 100 g of water. To convert this to molal solubility, we need to determine the number of moles of N2O in 0.121 g.

The molar mass of N2O can be found by adding the atomic masses of nitrogen (N) and oxygen (O). The atomic masses are:

Atomic mass of N = 14.01 g/mol
Atomic mass of O = 16.00 g/mol

Molar mass of N2O = (2 * 14.01 g/mol) + (1 * 16.00 g/mol)
= 28.02 g/mol + 16.00 g/mol
= 44.02 g/mol

Now, we can calculate the number of moles of N2O in 0.121 g:

Number of moles = Mass / Molar mass
= 0.121 g / 44.02 g/mol
≈ 0.00275 mol

Next, we can calculate the molal solubility by dividing the number of moles of N2O by the mass of the water in kilograms. The mass of the water can be calculated using the given percentage:

Mass of water = 100 g - 0.121 g
= 99.879 g

Converting the mass of water to kilograms:

Mass of water = 99.879 g / 1000 g/kg
= 0.099879 kg

Now, we can calculate the molal solubility:

Molal solubility = Number of moles / Mass of water (in kg)
= 0.00275 mol / 0.099879 kg
≈ 0.0275 mol/kg

So, the molal solubility of nitrous oxide in water at 1.600 atm and 20 oC is approximately 0.0275 mol/kg.