Problem 93 - Chemistry: Principles and Reactions

Question

An alloy made up of tin and copper is prepared by simultaneously electroplating the two metals from a solution containing \(\mathrm{Sn}\left(\mathrm{NO}_{3}\right)_{2}\) and \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\). If \(20.0 \%\) of the total current is used to plate tin, while \(80.0 \%\) is used to plate copper, what is the percent composition of the alloy?

Step-by-Step Solution

Answer

Answer: The percent composition of the alloy is approximately 20.0% tin and 80.0% copper.

Step 1: Find the mass of plated tin and copper

To begin, we can assume 1 coulomb (1C) of charge has been passed through the solution. Since 20.0% of current is used for tin, and 80.0% for copper, we can calculate the charge passed for each metal as follows: Charge for tin = 0.20 * 1C = 0.2C Charge for copper = 0.80 * 1C = 0.8C Furthermore, we know that the charge (Q) passed can be related to the mass (m) of the element plated according to the Faraday's law of electrolysis: Q = n * F where n is the total moles of the element plated and F is the Faraday's constant (96485 C/mol).

Step 2: Find the moles of both tin and copper plated

To calculate the moles of tin and copper, we can use the following equations: n_tin = Q_tin / F_tin n_copper = Q_copper / F_copper Plugging in the values, we have: n_tin = 0.2C / 96485 C/mol = 2.071\times10^{-6} mol n_copper = 0.8C / 96485 C/mol = 8.284\times10^{-6} mol

Step 3: Find the mole ratios for tin and copper

Now we will find the mole ratios of tin and copper in the alloy: Mole ratio(Tin: Copper) = n_tin : n_copper = 2.071\times10^{-6} mol : 8.284\times10^{-6} mol

Step 4: Calculate the percent composition of tin and copper in the alloy

To find the percent composition of the alloy, we can convert the mole ratio of tin and copper into percent as: Percent_tin = [(n_tin) / (n_tin + n_copper)] * 100% Percent_copper = [(n_copper) / (n_tin + n_copper)] * 100% Plugging the values, we get: Percent_tin = (2.071\times10^{-6} mol / (2.071\times10^{-6} mol + 8.284\times10^{-6} mol)) * 100% ≈ 20.0% Percent_copper = (8.284\times10^{-6} mol / (2.071\times10^{-6} mol + 8.284\times10^{-6} mol)) * 100% ≈ 80.0% So, the percent composition of the alloy is approximately 20.0% tin and 80.0% copper.

Key Concepts

Electroplating

Electroplating is often like a bit of magic in the world of science—it's a process where one metal is deposited onto the surface of another by using electricity. Imagine it like giving metal objects a new outfit through an electrically charged bath. In the exercise, an alloy made of tin and copper is created using electroplating from a solution containing their respective nitrates.

During electroplating, positive ions of the metal from the solution are attracted to a negatively charged electrode, called the cathode. This is where the actual 'plating' happens. On the other side, at the anode, the metal of the electrode is oxidized and wears away eventually, letting its ions into the solution. This keeps the metal ion concentration steady and the magic going.

Why Electroplate?

• To prevent corrosion of metals
• Improve appearance with gleaming metal coats
• Increase thickness of metal surfaces
• Enhance electrical conductivity, like in electronic components

The solution's makeup and the current distribution, which in this case is 20% for tin and 80% for copper, control the precise blend of metals in the alloy's final wardrobe.

Faraday's Law of Electrolysis

Now let's talk about Faraday's law of electrolysis. This rule helps us understand the relationship between the electric charge passed through the solution and the amount of substance that is electrolyzed. The key takeaway: every coulomb of charge results in a fixed amount of chemical change, just like every hour of work yields a fixed wage.

Michael Faraday, a superstar in the science world, laid down two laws for this. The first one says that the amount of substance deposited at each electrode is directly proportional to the charge passed through the electrolyte. So, if you use more charge, you get more of the metal at the cathode. The second law states that the amounts of different substances deposited by the same charge are proportional to their chemical equivalent weights.

Math Behind the Magic

Faraday figured out a constant, aptly called Faraday's constant (\(F\)), which is about 96,485 coulombs per mole. Tying in with the exercise, you calculate the moles of tin and copper using the charge (the electric 'juice') and Faraday's constant. The formula looks like this: \[Q = n \times F\]where \(Q\) is the electric charge and \(n\) is the number of moles of the metal deposited. This is the exact science spell used to find how much tin and copper make up the alloy—in moles, not just percentages.

Mole Ratios

Let's finish with mole ratios, a term that can sometimes make students sweat a bit. It's essentially a comparison of how much of one substance is present compared to another in a reaction or mixture—in this case, the alloy of tin and copper. Think of it like a cookie recipe: the ratio of flour to sugar helps determine the type of cookie you're making.

In chemistry, the mole ratio tells you how proportions of substances relate to each other based on the number of moles. It defines the stochiometry of a reaction and helps predict the outcome of an experiment.

From Moles to Percentages

Once we know the moles of tin and copper from the exercise solution, we can find their ratio, and with some simple math, we convert these mole ratios to percent composition of our alloy. This method is fundamental because it's how we express the makeup of mixtures in chemistry. And in the context of our alloy, it's how we dress it up in its shiny metal ratios, knowing exactly how much of each metal it's wearing, all thanks to the link between the charge used in electroplating and Faraday's prediction of how much metal you'll get.