Problem 14 - Chemistry: An Atoms-Focused Approach

Question

Tin(IV) chloride is prepared by the following combination reaction: $$\mathrm{Sn}(s)+2 \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SnCl}_{4}(\ell)$$ If \(x\) grams of chlorine combine with \(y\) grams of tin to form \(\operatorname{tin}(\mathrm{IV})\) chloride, how many grams of chlorine are there in a sample of \(\operatorname{tin}(\mathrm{II})\) chloride that contains \(y\) grams of tin?

Step-by-Step Solution

Answer

Answer: There are \(\frac{y \times 70.9}{118.71}\) grams of chlorine in a tin(II) chloride sample containing \(y\) grams of tin.

Step 1: Write down the given information

We are given that \(x\) grams of chlorine react with \(y\) grams of tin to form tin(IV) chloride. Also, we want to find out how many grams of chlorine are in a tin(II) chloride sample that contains \(y\) grams of tin.

Step 2: Write the balanced equation for tin(II) chloride

Just like the formation of tin(IV) chloride, we can write the formation of tin(II) chloride as: $$\mathrm{Sn}(s)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{SnCl}_{2}(s)$$

Step 3: Find the molar mass of tin and chlorine

From the periodic table, the molar mass of tin (Sn) is approximately 118.71 g/mol, and the molar mass of chlorine (Cl) is approximately 35.45 g/mol.

Step 4: Determine the moles of tin and chlorine in tin(IV) chloride

Using the balanced equation for tin(IV) chloride, we know that 1 mole of Sn reacts with 2 moles of Cl2. Therefore, the moles of tin (\(\mathrm{Sn}\)) is: $$\mathrm{moles \ of \ Sn} = \frac{y}{118.71}$$ The moles of chlorine in tin(IV) chloride (\(\mathrm{Cl_{2}}\)) is: $$\mathrm{moles \ of \ Cl_{2, IV}} = 2 \times \frac{y}{118.71}$$

Step 5: Determine the moles of chlorine in tin(II) chloride

From the stoichiometry of the balanced equation for tin(II) chloride, we know that 1 mole of Sn reacts with 1 mole of Cl2. Therefore, the moles of Cl2 in tin(II) chloride will be exactly the same as the moles of Sn, which is: $$\mathrm{moles \ of \ Cl_{2, II}} = \frac{y}{118.71}$$

Step 6: Calculate the mass of chlorine in tin(II) chloride

To find the mass of chlorine in tin(II) chloride, we can multiply the moles of Cl2 in tin(II) chloride by the molar mass of Cl2: $$\mathrm{mass \ of \ Cl_{2, II}} = \frac{y}{118.71} \times (2 \times 35.45) = \frac{y \times 70.9}{118.71}$$ Therefore, there are \(\frac{y \times 70.9}{118.71}\) grams of chlorine in a tin(II) chloride sample containing \(y\) grams of tin.

Key Concepts

Chemical Reactions

Chemical reactions involve a process where substances, known as reactants, undergo transformation to form new substances, called products. This transformation is represented by a chemical equation, which is a symbolic description of the reaction using chemical formulas. In the case of the formation of tin(IV) chloride, the chemical equation is \( \mathrm{Sn}(s) + 2 \mathrm{Cl}_{2}(g) \rightarrow \mathrm{SnCl}_{4}(\ell) \). Here, metallic tin (Sn) and chlorine gas (\( \mathrm{Cl}_{2} \)) combine in a fixed ratio to form tin(IV) chloride as the product.

Chemical equations must always be balanced to reflect the law of conservation of mass. This means that the number of atoms of each element in the reactants must equal the number in the products. For example, in the given equation, one mole of tin reacts with two moles of chlorine to maintain the balance of atoms on both sides of the reaction. Balancing equations helps us understand the stoichiometry of the reaction, which explains the quantitative relationships between the amounts of reactants and products needed in a reaction.

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a given substance. It is expressed in grams per mole (g/mol) and can be determined using the atomic masses of each element found in a periodic table. For instance, the molar mass of tin (Sn) is approximately 118.71 g/mol, while that of chlorine (Cl) is approximately 35.45 g/mol. When calculating the molar mass of molecules, such as diatomic chlorine gas (\( \mathrm{Cl}_2 \)), we add up the molar masses of its constituent atoms, resulting in \( 2 \times 35.45 = 70.9 \) g/mol.

Understanding molar mass is crucial for performing stoichiometric calculations, as it allows us to interconvert between moles and grams. Once we know the molar mass of a substance, we can determine the number of moles given a certain mass by using the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). This conversion is critical when using a balanced chemical equation to calculate the amounts of reactants needed or products formed in a chemical reaction.

Chlorine

Chlorine is a highly reactive halogen element that is often found in nature as part of a compound. It plays a significant role in many chemical reactions, particularly those occurring in industrial and laboratory settings. In its elemental form, chlorine exists as a diatomic molecule with the chemical formula \( \mathrm{Cl}_2 \), which exhibits a pale yellow-green color and a pungent odor.

Chlorine is used extensively in synthesis reactions, where it can combine with metals, such as tin, to form chlorides. These reactions are often redox processes, where chlorine typically acts as an oxidizing agent, gaining electrons from the other substance involved in the reaction. In the case of the creation of tin(IV) chloride, chlorine gas oxidizes metallic tin to form \( \mathrm{SnCl}_{4} \).

Due to its reactivity, chlorine must be handled with care. It is toxic and can cause harm if inhaled or if it comes into contact with skin. Safety measures should always be observed when working with chlorine, particularly in its gaseous form.