A sample consisting of various gases contains 2.6 10-6 mole fraction of radon. This gas at a total pressure of 37 atm is shaken with water at 30°C. Calculate the molar concentration of radon in the water.

Can somepne please provide a step by step instruction?

Sure! Here are the step-by-step instructions to calculate the molar concentration of radon in water:

Step 1: Calculate the partial pressure of radon gas.
- To do this, multiply the total pressure of the gas mixture with the mole fraction of radon.
- Given that the mole fraction of radon is 2.6 x 10^(-6) and the total pressure is 37 atm, the partial pressure of radon can be calculated as:
Partial Pressure of Radon = Mole Fraction of Radon x Total Pressure
= (2.6 x 10^(-6)) x 37 atm

Step 2: Convert the partial pressure of radon to concentration in moles per liter.
- To convert the partial pressure to concentration, we need to use Henry's law.
- Henry's law states that the concentration of gas in a liquid is directly proportional to its partial pressure.
- Mathematically, the concentration (C) is equal to the Henry's law constant (k) multiplied by the partial pressure (P) of the gas.
- The value of k depends on the temperature and the gas being dissolved.
- Since we know the temperature (30°C) and the gas being dissolved (radon), we can look up the value of the Henry's law constant (k) for radon in water at that temperature.
- Let's assume the value of k for radon in water at 30°C is 0.05 M/atm.
- Using this value, we can calculate the molar concentration (C) as:
Concentration of Radon = Henry's Law Constant x Partial Pressure of Radon
= 0.05 M/atm x [result of Step 1]

Step 3: Note that 1 atm is equal to 0.0821 L × atm/(K × mol) (gas constant - R).
- Convert the pressure from atm to L × mmHg/(K × mol) by dividing the given pressure by the gas constant (0.0821 L × atm/(K × mol)) to get the pressure in mmHg.
- Multiply the result by 22.414 to convert atm to mmHg.

Step 4: Convert the partial pressure from mmHg to moles per liter.
- To do this, divide the partial pressure (in mmHg) by the product of the gas constant (0.0821 L × atm/(K × mol)) and the temperature in Kelvin (30°C + 273.15).

Finally, after following these steps, the calculated value will give you the molar concentration of radon in water.

partial pressure = k*c

with c in moles/L.
You don't provide a k and I don't know it by memory; however, look up k (k is available in many different units--for this formula you want k in units of atm*L/mol which is the same as atm/M). To obtain partial pressure of the Rn it is mole fraction Rn*total P.