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.
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To calculate the molal solubility of nitrous oxide (N2O) in water at 1.600 atm and 20 oC, we need to use Henry's law. Henry's law states that the concentration of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
First, let's find Henry's law constant, which is the proportionality constant between the concentration of a gas in a liquid and the partial pressure of the gas. We can use the given solubility data to find this constant.
Given:
Enthalpy of solution of N2O in water, ΔHsol = -12 kJ/mol
Solubility of N2O at 20 oC and 1.00 atm = 0.121 g per 100 g of water
To find Henry's law constant (kH) at 20 oC and 1.00 atm, we can use the equation:
ΔHsol = -RT * ln(kH)
where R is the gas constant (8.314 J/(mol·K)) and T is the temperature in Kelvin (20 oC = 293.15 K). Converting ΔHsol to J/mol: -12 kJ/mol = -12000 J/mol. Plugging in the values:
-12000 J/mol = -8.314 J/(mol·K) * 293.15 K * ln(kH)
Now we can solve for kH:
ln(kH) = -12000 J/mol / (-8.314 J/(mol·K) * 293.15 K)
ln(kH) = 5.749
kH = e^(5.749) = 313.343 mol/(L·atm)
Now that we have the Henry's law constant, we can use it to calculate the molal solubility of N2O in water at 1.600 atm and 20 oC.
Given:
Partial pressure of N2O, P = 1.600 atm
Temperature, T = 20 oC = 293.15 K
Using Henry's law:
C = kH * P
where C is the concentration of the gas in the liquid in mol/L. Remember that molal solubility is defined as the moles of solute per kilogram of solvent.
Since we want the molal solubility (mol/kg), and we are starting with the mol/L concentration, we need to calculate the density of the water at 20 oC. The density of water at 20 oC is approximately 0.998 g/mL.
The molar mass of water (H2O) is 18.015 g/mol.
To calculate the molal solubility, we can use the following steps:
1. Calculate the concentration of N2O in mol/L (C):
C = kH * P
2. Convert the concentration from mol/L to mol/kg:
C_mol/kg = C * (density of water / molar mass of water)
Now let's calculate the molal solubility:
1. Calculate the concentration of N2O in mol/L (C):
C = kH * P = 313.343 mol/(L·atm) * 1.600 atm = 501.349 mol/L
2. Calculate the molal solubility (C_mol/kg):
C_mol/kg = C * (density of water / molar mass of water)
= 501.349 mol/L * (0.998 g/mL / 18.015 g/mol)
= 27.749 mol/kg
Therefore, the molal solubility of nitrous oxide (N2O) in water at 1.600 atm and 20 oC is approximately 27.749 mol/kg.