Question

Solder is a lead-tin alloy. \(1.00\) gram of the alloy treated with warm \(30 \% \mathrm{HNO}_{3}\) gave a lead nitrate solution and some insoluble white residue. After drying, the white residue weighed \(0.600 \mathrm{~g}\) and was found to be \(\mathrm{SnO}_{2}\). What was the percentage tin in the sample? \(\mathrm{Sn}+4 \mathrm{HNO}_{3}+\mathrm{SnO}_{2}+4 \mathrm{~N}_{2}+2 \mathrm{H}_{2} \mathrm{O}\)

Short answer

The percentage of tin in the sample is 47.4%. To find this, we first determined the mass of Sn in the 0.600 g of SnO2 using the balanced chemical reaction, which was 0.474 g Sn. Then, we divided the mass of Sn by the mass of the entire sample (1.00 g) and multiplied by 100 to get 47.4%.

Step-by-step solution

Write down the balanced chemical reaction

We are given the balanced chemical reaction: \(\mathrm{Sn} + 4 \mathrm{HNO}_{3} \rightarrow \mathrm{SnO}_{2} + 4 \mathrm{NO}_{2} + 2 \mathrm{H}_{2}\mathrm{O}\).

Use the mass of SnO2 to find the mass of Sn

From the balanced chemical reaction, we can see that 1 mole of Sn produces 1 mole of SnO2. Using the molar masses of Sn (118.7 g/mol) and SnO2 (150.7 g/mol), we can find the mass of Sn present in the 0.600 g of SnO2: \(118.7 \text{ g Sn} \cdot \frac{\text{1 mol Sn}}{\text{1 mol SnO}_{2}} \cdot \frac{0.600 \text{ g SnO}_{2}}{150.7 \text{ g SnO}_{2}} = 0.474 \text{ g Sn}\).

Determine the mass of the entire sample

We are given the mass of the solder alloy, which is 1.00 g.

Calculate the percentage of tin in the sample

To find the percentage of tin in the sample, divide the mass of Sn (0.474 g) by the mass of the sample (1.00 g) and multiply by 100: \(\frac{0.474 \text{ g Sn}}{1.00 \text{ g sample}} \cdot 100\% = 47.4\%\). The percentage of tin in the sample is 47.4%.

Key concepts

Solder Alloy

A solder alloy is a fusion of two or more metals, in this case, lead and tin. This metallic blend is widely used in electronics and plumbing for its ability to join together metal surfaces. Tin's low melting point combines with other metals to lower the overall melting temperature, enabling these alloys to be melted and applied at lower temperatures than their component metals might otherwise require, which decreases the risk of damaging heat-sensitive components.
Understanding solder alloys, specifically lead-tin alloys, is essential for material engineers and technicians working in manufacturing sectors that require metal joining. This knowledge is also crucial for environmentally conscious designs, as the use of lead has become restricted under regulations such as RoHS (Restriction of Hazardous Substances) in the European Union.

Lead-Tin Alloy

Lead-tin alloy is another type of solder, often praised for its effective joining properties and ease of use. Despite the advantageous attributes of lead, like malleability, and tin, like corrosion resistance, the combination of these metals raises health and environmental concerns due to lead’s toxicity. Alternatives, like lead-free solder alloys, are gaining popularity. In this exercise, we deal with a typical analysis of lead-tin solder alloy to determine its composition, which is vital for understanding its physical properties and suitability for specific applications.
Given a specific case where the alloy is treated to retrieve its constituents, we process the resultant products through stoichiometric principles, lending practical insight into metallurgical analysis and recycling methods.

Molar Mass

The concept of molar mass is fundamental in chemistry and is defined as the mass of one mole of any substance (expressed in grams per mole, g/mol). For elements, it is numerically equivalent to the atomic mass found on the periodic table. For compounds like SnO2 , the molar mass is the sum of the atomic masses of all atoms in the molecule.
Understanding molar mass allows us to transition between the mass of a substance and the number of moles, facilitating a plethora of calculations ranging from the creation of solutions with specific concentrations to stoichiometric calculations in chemical reactions. In the given exercise, it's used to convert the mass of SnO2 to the corresponding mass of Sn.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative aspects of chemical reactions. It allows us to predict the amounts of products and reactants in a chemical reaction using balanced chemical equations. Stoichiometry is hinged on the law of conservation of mass and the idea that elements are bound into compounds in fixed ratios.
Applied stoichiometry involves calculations based on the molar ratios of the reactants and products as given in a balanced chemical equation. In our exercise, stoichiometry is applied to infer the amount of tin from the measured amount of a tin oxide product, SnO2 , using the balanced chemical reaction as the guide to the fixed ratios.

Chemical Reaction

A chemical reaction is a process where reactants transform into products through breaking and forming of chemical bonds. These reactions are represented by chemical equations that indicate the substances involved and their stoichiometric ratios. The representation of these reactions is critical for predicting the outcomes of chemical processes.
In this case, tin reacts with nitric acid to form tin oxide and other by-products. The provided balanced equation allows us to see the conversion of tin into tin oxide clearly. This conversion ratio becomes the crux of the percentage composition calculation since it lets us directly relate the measured mass of the tin oxide to the original amount of tin from which it was produced.