Problem 74 - Introductory Chemistry Atoms First

Question

Consider the balanced chemical equation \(\mathrm{SCl}_{4}+2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{SO}_{2}+4 \mathrm{HCl}\) (a) How many grams of \(\mathrm{H}_{2} \mathrm{O}\) will react with \(5.000 \mathrm{~g}\) of \(\mathrm{SCl}_{4} ?\) (b) How many grams of \(\mathrm{SO}_{2}\) can you make from \(10.00 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} ?\) (c) Suppose you react \(5.000 \mathrm{~g}\) of \(\mathrm{SCl}_{4}\) with the amount of \(\mathrm{H}_{2} \mathrm{O}\) you calculated in part (a). How many grams of \(\mathrm{HCl}\) will you form?

Step-by-Step Solution

Answer

(a) 1.0116 g of H2O will react with 5.000 g of SCl4. (b) 17.81 g of SO2 can be made from 10.00 g of H2O. (c) 4.1026 g of HCl will be formed when 5 g of SCl4 react with 1.0116 g of H2O.

Step 1: Convert given mass into moles

First, calculate the molar mass of the substances involved. For SCl4: \( M_{SCl4} = 1*32.1 + 4*35.5 = 178.1 g/mol \), for H2O: \( M_{H2O} = 2*1.0 + 1*16.0 = 18.0 g/mol\), and for SO2: \( M_{SO2} = 1*32.1 + 2*16.0 = 64.1 g/mol \). Next, convert the mass of SCl4 and H2O into moles. For SCl4: \(n_{SCl4} = \frac{5.00\mathrm{~g}}{178.1\mathrm{~g/mol}} = 0.0281\mathrm{~mol}\) For H2O: \(n_{H2O} = \frac{10.00\mathrm{~g}}{18.0\mathrm{~g/mol}} = 0.5556\mathrm{~mol}\)

Step 2: Calculate moles of H2O needed for SCl4 reaction (part a)

From the balanced chemical equation, we can see that 1 mole of SCl4 requires 2 moles of H2O. So, to find the moles of water needed for 0.0281 moles of SCl4, we can create a ratio: \( n_{H2O} = 2 * n_{SCl4} = 2 * 0.0281\mathrm{~mol} = 0.0562\mathrm{~mol} \)

Step 3: Convert moles of H2O to grams (part a)

Convert the moles of H2O needed to grams using its molar mass: \(m_{H2O} = n_{H2O} * M_{H2O} = 0.0562\mathrm{~mol} * 18.0\mathrm{~g/mol} = 1.0116\mathrm{~g}\) So, 1.0116 g of H2O will react with 5.000 g of SCl4.

Step 4: Calculate moles of SO2 from H2O (part b)

The balanced chemical equation shows that 2 moles of H2O produce 1 mole of SO2. To find the moles of SO2 produced, we can create a ratio: \( n_{SO2} = \frac{1}{2} * n_{H2O}=\frac{1}{2} * 0.5556\mathrm{~mol} = 0.2778\mathrm{~mol} \)

Step 5: Convert moles of SO2 to grams (part b)

Convert the moles of SO2 to grams using its molar mass: \(m_{SO2} = n_{SO2} * M_{SO2} = 0.2778\mathrm{~mol} * 64.1\mathrm{~g/mol} = 17.81\mathrm{~g}\) Therefore, 17.81 g of SO2 can be made from 10.00 g of H2O.

Step 6: Calculate moles of HCl in the reaction (part c)

The balanced chemical equation shows that 1 mole of SCl4 produces 4 moles of HCl. So, 0.0281 moles of SCl4 will produce: \( n_{HCl} = 4 * n_{SCl4} = 4 * 0.0281\mathrm{~mol} = 0.1124\mathrm{~mol} \)

Step 7: Convert moles of HCl to grams (part c)

Use HCl molar mass (M=36.5 g/mol) to convert moles to grams: \( m_{HCl} = n_{HCl} * M_{HCl} = 0.1124\mathrm{~mol} * 36.5\mathrm{~g/mol} = 4.1026\mathrm{~g} \) So, 4.1026 g of HCl will be formed when 5 g of SCl4 react with the calculated 1.0116 g of H2O.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances, called reactants, are transformed into different substances, called products. In a chemical reaction, bonds between atoms in the reactants are broken, and new bonds are formed in the products.
For example, in the reaction given by the equation \( \mathrm{SCl}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{SO}_{2} + 4 \mathrm{HCl} \), sulfur tetrachloride (\( \mathrm{SCl}_{4} \)) reacts with water (\( \mathrm{H}_{2} \mathrm{O} \)) to produce sulfur dioxide (\( \mathrm{SO}_{2} \)) and hydrogen chloride (\( \mathrm{HCl} \)).
Understanding chemical reactions involves knowing how substances interact and transform, which is crucial in fields like chemistry, biology, and environmental science.

Mole Concept

The mole concept is a fundamental chemical principle used to express the amount of a substance. One mole contains exactly \( 6.022 \times 10^{23} \) entities (Avogadro's number), such as atoms, molecules, or ions.
In practical terms, the mole concept allows chemists to count particles by weighing them. For instance, calculating how many moles of \( \mathrm{H}_{2} \mathrm{O} \) are in a reaction helps determine how much product will form or how much reactant is needed.
By translating mass to moles through molar mass, we can accurately study the relationships in reactions and ensure precise chemical calculations.

Balanced Chemical Equations

Balanced chemical equations are vital for describing the proportions of reactants and products in a chemical reaction.
Each element must have the same number of atoms on both sides of the equation to comply with the conservation of mass.
For instance, in \( \mathrm{SCl}_{4} + 2 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{SO}_{2} + 4 \mathrm{HCl} \), sulfur, chlorine, hydrogen, and oxygen atoms are balanced in respective quantities, ensuring that the equation faithfully represents the true nature of the reaction.
Balancing equations is crucial for predicting the outcomes of reactions and for calculating how much of a substance will be consumed or produced.

Molar Mass

Molar mass is defined as the mass of one mole of a substance, expressed in grams per mole (g/mol). Each chemical element has a unique molar mass based on its atomic mass, found on the periodic table.
For example, the molar mass of \( \mathrm{H}_{2} \mathrm{O} \) is 18.0 g/mol, and likewise \( \mathrm{SCl}_{4} \) is 178.1 g/mol.
Knowing the molar mass allows chemists to convert between grams and moles, facilitating calculations that involve quantities of substances participating in chemical reactions. Accurate measurement of quantities in chemical formulas and reactions depends on correctly calculated molar masses.

Mass-to-Mole Conversion

Mass-to-mole conversion is a technique based on the molar mass, allowing us to translate a given mass of a substance into an equivalent amount in moles.
The formula for this conversion is \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass in grams, and \( M \) is the molar mass.
This is essential when calculating the moles of reactants needed or products formed in a reaction, such as converting 5.000 g of \( \mathrm{SCl}_{4} \) to moles to find how much \( \mathrm{H}_{2} \mathrm{O} \) is needed to react with it. Using mass-to-mole conversion provides a bridge between the macroscopic and molecular scales, making stoichiometric calculations possible.