Problem 110 - Chemistry Matter and Change

Question

Determine the mass in grams of each element. a. \(1.33 \times 10^{22} \mathrm{mol}\) of \(\mathrm{Sb}\) b. \(4.75 \times 10^{14} \mathrm{mol}\) of \(\mathrm{Pt}\) c. \(1.22 \times 10^{23} \mathrm{mol}\) of Ag d. \(9.85 \times 10^{24} \mathrm{mol}\) of Cr

Step-by-Step Solution

Answer

a. Mass of Sb = \(1.62 \times 10^{24}\) g b. Mass of Pt = \(9.26 \times 10^{16}\) g c. Mass of Ag = \(1.32 \times 10^{25}\) g d. Mass of Cr = \(5.12 \times 10^{26}\) g

Step 1: Find the molar mass of Sb

Look up the molar mass of Sb (Antimony) on the periodic table. The molar mass of Sb is 121.76 g/mol.

Step 2: Multiply moles by molar mass

Multiply the given moles of Sb (1.33 × 10²² mol) by its molar mass (121.76 g/mol) to find the mass in grams: Mass of Sb = \(1.33 \times 10^{22} \mathrm{mol} \times 121.76 \frac{\mathrm{g}}{\mathrm{mol}}\) b. Calculate the mass of Pt

Step 1: Find the molar mass of Pt

Look up the molar mass of Pt (Platinum) on the periodic table. The molar mass of Pt is 195.08 g/mol.

Step 2: Multiply moles by molar mass

Multiply the given moles of Pt (4.75 × 10¹⁴ mol) by its molar mass (195.08 g/mol) to find the mass in grams: Mass of Pt = \(4.75 \times 10^{14} \mathrm{mol} \times 195.08 \frac{\mathrm{g}}{\mathrm{mol}}\) c. Calculate the mass of Ag

Step 1: Find the molar mass of Ag

Look up the molar mass of Ag (Silver) on the periodic table. The molar mass of Ag is 107.87 g/mol.

Step 2: Multiply moles by molar mass

Multiply the given moles of Ag (1.22 × 10²³ mol) by its molar mass (107.87 g/mol) to find the mass in grams: Mass of Ag = \(1.22 \times 10^{23} \mathrm{mol} \times 107.87 \frac{\mathrm{g}}{\mathrm{mol}}\) d. Calculate the mass of Cr

Step 1: Find the molar mass of Cr

Look up the molar mass of Cr (Chromium) on the periodic table. The molar mass of Cr is 51.9961 g/mol.

Step 2: Multiply moles by molar mass

Multiply the given moles of Cr (9.85 × 10²⁴ mol) by its molar mass (51.9961 g/mol) to find the mass in grams: Mass of Cr = \(9.85 \times 10^{24} \mathrm{mol} \times 51.9961 \frac{\mathrm{g}}{\mathrm{mol}}\)

Key Concepts

Moles to Grams Conversion

Converting from moles to grams is a common process in chemistry. It is essential for calculating the mass of elements or compounds when given the amount in moles. This conversion allows chemists to work with measurable quantities, as grams are a practical unit for weighing substances.
Understanding the conversion involves two key ideas:

• Molar Mass: This is the mass of one mole of a substance (element or compound) and is expressed in grams per mole (g/mol).
• Mathematical Conversion: To find the mass in grams, multiply the number of moles by the molar mass of the element or compound.

For example, if you have 1 mole of Antimony (Sb), you know from the periodic table that its molar mass is 121.76 g/mol, so 1 mole weighs 121.76 grams. If given a different amount in moles, multiply that number by 121.76 to find the grams.
This conversion is proportional because 1 mole always represents the same number of atoms, Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles/mole. By using the molar mass for conversion, you're able to directly translate moles, a count of particles, into grams, a measurable mass.

Chemical Elements

Chemical elements are substances consisting of one type of atom. There are around 118 known elements, each with its own unique properties. They serve as the building blocks of matter and cannot be broken down into simpler substances by ordinary chemical means.
Every element is characterized by:

• Atomic Number: The number of protons in the nucleus, which determines the element's identity.
• Symbol: A one or two-letter abbreviation often based on either Latin or English names of the elements (e.g., Sb for Antimony, Pt for Platinum).
• Molar Mass: The mass of one mole of the element's atoms, often appearing in atomic mass units (amu) but used as grams per mole in calculations.

This information not only helps in moles to grams conversions but is also fundamental in understanding chemical reactions and properties. Knowing an element's atomic number and symbol helps easily locate it on the periodic table, enhancing comprehension and application in scientific studies.

Periodic Table

The periodic table is a systematic arrangement of the chemical elements. It's an incredibly useful tool for anyone studying chemistry or related sciences.
Several important features make the periodic table essential:

• Organization: Elements are arranged in rows called periods and columns called groups or families. This layout reflects recurring properties and trends across the table.
• Element Placement: Each element's position provides clues about its characteristics such as electronegativity, ionization energy, and atomic radius.
• Groups and Periods: Elements in the same group share similar chemical behaviors. Moving across a period, properties change predictably, such as increasing atomic number.

The table is also where you find essential information, such as the molar mass needed for conversions, like those from moles to grams. This organized display not only aids in calculations but also helps in understanding the relationships and reactivity of elements, making it indispensable for chemical analyses.