Question

A \(1.50 \mathrm{~g}\) sample of type metal (an alloy of \(\mathrm{Sn}, \mathrm{Pb}, \mathrm{Cu}\) and \(\mathrm{Sb}\) ) is dissolved in nitric acid, and metastannic acid, \(\mathrm{H}_{2} \mathrm{SnO}_{3}\), precipitates. This is dehydrated by heating to tin (IV) oxide, which is found to weigh \(0.50 \mathrm{~g}\). What percentage of tin was in the original type metal sample? \((\mathrm{Sn}=119)\) (a) \(33.33 \%\) (b) \(26.27 \%\) (c) \(29.38 \%\) (d) \(52.54 \%\)

Short answer

The percentage of tin in the original type metal sample is 29.38%.

Step-by-step solution

Understand the Problem

We are given a 1.50g sample of an alloy. When this alloy is processed, tin (IV) oxide (SnO2) is obtained which weighs 0.50g. We need to calculate the percentage of tin (Sn) in the original sample. We know that in tin (IV) oxide, tin is in its +4 oxidation state, meaning each tin atom is associated with two oxygen atoms.

Calculate the amount of tin in tin (IV) oxide

In SnO2, the atomic weight of Sn is 119g/mol and that of O is 16g/mol. Therefore, one mole of SnO2 has a mass of (119 + 2*16)g = 151g. The moles of Sn in 0.50g of SnO2 can be calculated by the ratio (0.50g SnO2 * (1 mol Sn / 151g SnO2)). We find the mass of Sn by multiplying the moles of Sn by its atomic weight (119g/mol).

Calculate the percentage of tin in the sample

We now take the mass of Sn (from Step 2) and divide it by the mass of the original sample (1.50g), then multiply by 100 to find the percentage.

Key concepts

Quantitative Analysis in Chemistry

Quantitative analysis in chemistry refers to the techniques used to determine the amount or concentration of a substance within a mixture or sample. These methods provide information about the quantity in terms of weight or volume in rigorous numerical terms. One of the quintessential applications of quantitative analysis is in ascertaining the composition of substances, as seen in our textbook exercise where we measure the percentage of tin in an alloy.

For chemicals composed of elements, the percentage composition is particularly crucial as it reveals the proportion of each element in a compound. This can be determined through various means, such as through a series of chemical reactions leading to a form that can be easily measured, like the precipitation and subsequent dehydration to tin (IV) oxide in the provided exercise. This approach is vital in fields like materials science and metallurgy where the characteristics of an alloy—such as hardness, melting point, and reactivity—are directly linked to its elemental composition.

Chemical Calculations

Chemical calculations form the backbone of many scientific disciplines, allowing for the precise quantification of substances involved in chemical reactions. They encompass techniques such as determining molar masses, conversion between moles and grams, and using stoichiometric ratios to infer amounts from balanced equations. In the exercise, these calculations begin with the assessment of the molar mass of tin (IV) oxide and proceed to deduce the amount of tin within it.

Understanding the molar mass concept is critical; it signifies the weight of one mole (Avogadro's number of particles) of a substance. Here, the students would employ the molar mass to convert the given weight of tin (IV) oxide into moles, a fundamental unit in chemistry that allows for the comparison of substances on an equal basis. The calculations herein are precise and methodical, showing the significant role they play in determining the percentage of an element in a compound.

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the calculation of the reactants and products in chemical reactions. It is crucial for predicting yields and for scaling reactions up or down in both laboratory and industrial settings. It also includes the principle that matter is neither created nor destroyed during a chemical reaction (the Law of Conservation of Mass).

In context to our problem, stoichiometry involves using the known stoichiometric relationships in the compound tin (IV) oxide to calculate the amount of tin metal present in the sample. By understanding the fixed ratio of tin to oxygen in the compound, we can utilize the weight of the tin (IV) oxide to uncover the weight of just the tin. This example illustrates the application of stoichiometry in a real-world scenario - from knowing the weight of a certain product, one can work backwards to find out how much of a specific reactant was initially there, an indispensable stoichiometric calculation for chemists everywhere.