The molar conductivities at infinite dilution for , , , , and at 300 K are 260, 308, 150, 426, and 105 S cm mol , respectively. We need to calculate the molar conductivity at infinite dilution ( ) for formic acid (HCOOH) in the same units. Using Kohlrausch’s law, the molar conductivity at infinite dilution of an electrolyte is the sum of the ionic molar conductivities of its ions, weighted by their stoichiometric coefficients: where and are the number of cations and anions per formula unit, and and are the ionic molar conductivities at infinite dilution. Formic acid (HCOOH) dissociates as: Thus, (for ), (for ), and: We are given:
Our goal is to find and to compute .
Step 1: Apply Kohlrausch’s Law to Each Electrolyte
For each electrolyte, we write the molar conductivity as the sum of the ionic conductivities:
- Na SO : Dissociates as :
- K SO : Dissociates as :
- KCl: Dissociates as :
- HCl: Dissociates as :
- HCOONa: Dissociates as :
Step 2: Calculate Ionic Conductivities
We need and . Let’s solve for these using the given equations.
Find :} From the equation for HCOONa: We need . Use the equations for Na SO and K SO to find : Subtract (1) from (2) to eliminate : Now, use the equation for KCl: We need . Let’s find using HCl: We don’t have yet, so let’s try to find and first. From (6): Substitute into (3): Now we have two equations involving : To find , we need . Let’s find and to proceed. Substitute into the equation for K SO and combine with Na SO . Instead, let’s try to find and directly.
Find and :
From HCl: From KCl: We need . Use (6) and solve later. Let’s try to find and first. Subtract (7) from (5): Substitute into (7): This is consistent with (5). Let’s find using (3) and (8): Now use (6): Substitute into (10): This matches (5), confirming consistency. Let’s find using Na SO and K SO . Substitute into (2): Compare with (1): This suggests we need to solve for and directly. Let’s try substituting known values. Assume: Use (8) in (4): Now we have: Let’s verify by calculating , , and .
Step 3: Verify Calculations
Assume , then from (5): From (8): From (6) and (3): Substitute into (3): This confirms consistency. Now use Na SO : For K SO : This is consistent. Now find : This confirms: Step 4: Final Answer The molar conductivity at infinite dilution for formic acid is: