In a moist room (44m3) 4 kg dry CaCl2 is placed. The room contains 10 g/m3 of H20. How much of the CaCl2 is converted to CaCl2*2H2O?
Temperature 10 deg C. Equilibrium constant is 10^5 atm-2 at 10 deg C.
I've caclulated Kp to 0,0032 atm and then tried to convert to Kc to 1,7089 mol/l. However this can't be right.
To solve this problem, we need to use the equilibrium constant and the given information to determine the amount of CaCl2 that is converted to CaCl2·2H2O. Let's break it down step by step:
Step 1: Write the balanced equation for the reaction.
The reaction between CaCl2 and H2O can be represented by the equation:
CaCl2 + H2O ↔ CaCl2·2H2O
Step 2: Determine the amount of water in moles.
Given that the room contains 10 g/m3 of H2O and the volume of the room is 44 m3, the total amount of water in moles can be calculated as follows:
Total moles of H2O = (10 g/m3) / (18.015 g/mol) × (44 m3) = 24.4 mol
Step 3: Calculate the initial concentration of CaCl2.
The mass of CaCl2 is given as 4 kg, so the initial moles of CaCl2 can be determined as:
Initial moles of CaCl2 = (4 kg) / (110.984 g/mol) = 36.1 mol
Step 4: Calculate the equilibrium concentration of CaCl2.
Let's assume that x moles of CaCl2 are converted to CaCl2·2H2O at equilibrium. Hence, the concentration of CaCl2 at equilibrium will be (36.1 - x) moles / 44 m3.
Step 5: Calculate Kc.
Now, we can use the equilibrium expression and the given temperature to calculate Kc.
Kc = [CaCl2·2H2O] / ([CaCl2] × [H2O])
= [CaCl2·2H2O] / ([36.1 - x] × [24.4])
= 10^5 atm^-2
Step 6: Convert Kc to Kp.
Since the number of moles of gas remains the same, the conversion between Kc and Kp is straightforward. At a temperature of 10°C, you can use the ideal gas law to convert the units:
Kp = Kc × (RT)^(Δn)
= Kc × (0.0821 atm·L/mol·K)^(2 - 1)
= Kc × 0.0821 atm·L/mol·K
Here, Δn is the difference in the number of moles of gas between the product side and the reactant side, which is 2 - 1 = 1.
In your calculations, if you have obtained a Kp value of 0.0032 atm, you can divide that value by 0.0821 atm·L/mol·K to find the corresponding Kc value.
Make sure to check your calculations and units to see if they match the correct values mentioned in the problem. Double-checking your work will help verify if your obtained value of Kc is correct or if there was an error in your calculations.