To Aqua solutions, one containing Silver Nitrate and other X + 2 ions I had electrolyzed with the same amount of current for equal times. 5 gram of silver and 3.17 gram of X are deposited that what is the molar mass of eggs if molecular weight of silver is 108?1)34.3 gram per mole2)68.4 gram per mole3)137 gram per mole4)170 gram per mole

To find the molar mass of the unknown ion X, we can use Faraday's laws of electrolysis, which relate the amount of substance deposited during electrolysis to the amount of electric charge passed through the electrolyte. In this case, we know the mass of silver deposited and its molar mass, which will help us deduce the molar mass of ion X.

Understanding Electrolysis and Molar Mass

When you electrolyze a solution containing ions, the amount of substance deposited at the electrodes is proportional to the quantity of electricity passed through the solution. The equation we can use is:

• Q = nF

Where Q is the electric charge (in coulombs), n is the number of moles of substance deposited, and F is Faraday's constant (approximately 96485 C/mol). Let's break down the process step by step.

Step 1: Calculate Moles of Silver Deposited

First, we can calculate the number of moles of silver deposited. We have:

• Mass of silver (Ag) = 5 grams
• Molar mass of silver = 108 g/mol

Using the formula:

• n = mass / molar mass

we can find:

• n(Ag) = 5 g / 108 g/mol ≈ 0.0463 mol

Step 2: Relate the Moles of X to Current

Now, let's consider the other ion X, which deposits 3.17 grams. We need to express the amount of current that produced this deposition. Since both reactions occurred over the same time with the same current, we can set up a ratio based on the charge.

• Assume X has a charge of +2 (X^2+), which means it would require 2 moles of electrons to deposit 1 mole of X.

Thus, for every mole of X deposited, it corresponds to 2 moles of electrons transferred. Let's define the moles of X deposited as n(X).

Step 3: Calculate Moles of X and Molar Mass

Now, we can express n(X) in terms of its mass:

• Let the molar mass of X be M.

Using the formula for moles:

• n(X) = mass of X / molar mass of X = 3.17 g / M

Since the charge for silver and X are equal, we can equate the charges:

• n(Ag) = 0.0463 mol
• n(X) / 2 = n(Ag) => n(X) = 2 * n(Ag)

So we have:

• n(X) = 2 * 0.0463 mol ≈ 0.0926 mol

Using this in the equation for moles of X, we get:

• 0.0926 mol = 3.17 g / M

Step 4: Final Calculation for M

Rearranging gives us:

• M = 3.17 g / 0.0926 mol ≈ 34.2 g/mol

Rounding this off gives us a molar mass of approximately 34.3 g/mol. Therefore, the molar mass of ion X is:

• 34.3 grams per mole

Conclusion

Thus, the answer to your question is that the molar mass of X is 34.3 g/mol, corresponding to option 1 in your list.