Question

Henry Law’s Constants at a system temperature of 25°C (77°F) of nitrogen is 1600 atm/(mol/litre). Molar weight of N2 is 28.0134 g/mol and partial fraction in air is ~ 0.79. Calculate the Nitrogen dissolved in the Water at atmospheric pressure.

(a) 0.0138 g/liter

(b) 0.0130 g/liter

(c) 0.0132 g/liter

(d) 0.0134 g/liter

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Answer 1

To calculate the amount of nitrogen dissolved in water at atmospheric pressure, we can apply Henry's Law, which states:

$$C=H\cdot P$$

Where:

• $C$ is the concentration of the gas dissolved in the liquid (in mol/L),
• $H$ is the Henry’s law constant (in atm·L/mol),
• $P$ is the partial pressure of the gas (in atm).

Given:

• Henry’s Law constant for nitrogen (H) = 1600 atm·L/mol
• Partial fraction of nitrogen in air = 0.79
• Atmospheric pressure = 1 atm
• Molar weight of nitrogen = 28.0134 g/mol

First, calculate the partial pressure of nitrogen in the air at atmospheric pressure:

PN2=Fraction of N2×Atmospheric PressureP_{N_2} = \text{Fraction of N}_2 \times \text{Atmospheric Pressure}PN2​​=Fraction of N2​×Atmospheric Pressure PN2=0.79×1 atm=0.79 atmP_{N_2} = 0.79 \times 1 \, \text{atm} = 0.79 \, \text{atm}PN2​​=0.79×1atm=0.79atm

Now, apply Henry’s law to calculate the concentration of nitrogen in the water:

C=H⋅PN2=1600 atm\cdotpL/mol×0.79 atm=1264 mol/LC = H \cdot P_{N_2} = 1600 \, \text{atm·L/mol} \times 0.79 \, \text{atm} = 1264 \, \text{mol/L}C=H⋅PN2​​=1600atm\cdotpL/mol×0.79atm=1264mol/L

Now, to convert the concentration from mol/L to g/L, use the molar mass of nitrogen (28.0134 g/mol):

Mass of N2=C×Molar mass=1264 mol/L×28.0134 g/mol\text{Mass of N}_2 = C \times \text{Molar mass} = 1264 \, \text{mol/L} \times 28.0134 \, \text{g/mol}Mass of N2​=C×Molar mass=1264mol/L×28.0134g/mol Mass of N2=35.44 g/L\text{Mass of N}_2 = 35.44 \, \text{g/L}Mass of N2​=35.44g/L

Thus, none of the provided answer choices match the value calculated, suggesting there may be a misunderstanding in the question's data interpretation. However, if you intended to solve for oxygen solubility with similar principles, the approach would be similar to the above!