Problem 30 - Chemistry and Chemical Reactivity

Question

Calculate the amount (moles) represented by each of the following: (a) \(16.0 \mathrm{g}\) of \(\mathrm{Na}\) (b) 0.876 g of tin (c) \(0.0034 \mathrm{g}\) of platinum (d) \(0.983 \mathrm{g}\) of \(\mathrm{Xe}\)

Step-by-Step Solution

Answer

(a) 0.696 mol Na; (b) 0.00738 mol Sn; (c) 0.0000174 mol Pt; (d) 0.00749 mol Xe.

Step 1: Understanding the Concept

To determine the number of moles of a substance, we need the formula: \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass in grams, and \( M \) is the molar mass of the element in grams per mole.

Step 2: Calculation for Sodium (Na)

For sodium, the molar mass \( M \) is approximately \( 22.99 \ \text{g/mol} \). Using the formula: \[ n = \frac{16.0 \ \text{g}}{22.99 \ \text{g/mol}} \approx 0.696 \ \text{mol} \] Thus, there are approximately \( 0.696 \) moles of sodium in \( 16.0 \ \text{g} \).

Step 3: Calculation for Tin (Sn)

For tin, the molar mass \( M \) is approximately \( 118.71 \ \text{g/mol} \). Using the formula: \[ n = \frac{0.876 \ \text{g}}{118.71 \ \text{g/mol}} \approx 0.00738 \ \text{mol} \] This results in approximately \( 0.00738 \) moles of tin in \( 0.876 \ \text{g} \).

Step 4: Calculation for Platinum (Pt)

For platinum, the molar mass \( M \) is approximately \( 195.08 \ \text{g/mol} \). Using the formula: \[ n = \frac{0.0034 \ \text{g}}{195.08 \ \text{g/mol}} \approx 0.0000174 \ \text{mol} \] Hence, there are roughly \( 0.0000174 \) moles of platinum in \( 0.0034 \ \text{g} \).

Step 5: Calculation for Xenon (Xe)

For xenon, the molar mass \( M \) is approximately \( 131.29 \ \text{g/mol} \). Using the formula: \[ n = \frac{0.983 \ \text{g}}{131.29 \ \text{g/mol}} \approx 0.00749 \ \text{mol} \] Therefore, there are about \( 0.00749 \) moles of xenon in \( 0.983 \ \text{g} \).

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that relates the mass of a substance to the amount of each element in a mole. It is essentially the weight of one mole of a given substance, expressed in grams per mole (g/mol). To determine molar mass, you can add the atomic masses of all atoms present in a molecule or compound. For instance, for sodium (Na), the molar mass is about 22.99 g/mol.

• To find the molar mass, refer to the periodic table where each element's atomic mass is listed.
• The atomic mass is the average mass of atoms of an element, measured in atomic mass units (amu).
• Molar mass is vital in determining the number of moles, allowing chemists to perform calculations needed for chemical reactions.

By understanding and calculating molar mass, you can easily convert between the mass of a substance and the number of moles, facilitating various chemical calculations.

Chemical Calculation

Chemical calculation is an essential skill in chemistry, used to quantify amounts of substances involved in chemical reactions. One of the primary calculations involves converting mass to moles using the molar mass of a substance. This is achieved using the formula: \[ n = \frac{m}{M} \]Where:

• \( n \) = number of moles
• \( m \) = mass in grams
• \( M \) = molar mass in grams per mole

Understanding this formula allows you to determine how many moles are present in a given mass of a substance, which can then be used for various purposes such as preparing solutions and analyzing chemical reactions. Always start with identifying the molar mass from the periodic table to accurately use this formula in your calculations.

Stoichiometry

Stoichiometry involves the use of balanced chemical equations to calculate the amounts of reactants and products in a chemical reaction. It is a core concept in chemistry that requires a solid understanding of moles and molar mass. Here's how stoichiometry works:

• Write the balanced chemical equation for the reaction.
• Use the coefficients from the balanced equation to determine the mole ratio between reactants and products.
• Convert known quantities (mass) into moles, using the molar masses.
• Calculate the moles of other substances using the mole ratios from the balanced equation.

This approach allows chemists to predict how much of each substance is required or produced in a reaction. Stoichiometry is extremely useful for creating desired products efficiently and safely and is used widely in laboratories and industries.