Question

Which one of the following statements is/are correct? a. One mole of \(\mathrm{CH}_{4}\) and \(17 \mathrm{~g} \mathrm{NH}_{3}\) at NTP occupies same volume b. One gram mole of silver equals \(108 / 6.023 \times 10^{25} \mathrm{~g}\) c. One gram mole of \(\mathrm{CO}_{2}\) is \(6.023 \times 10^{23}\) times heavier than one molecule of \(\mathrm{CO}_{2}\) d. One mole Ag weighs more than that of two moles of Ca

Short answer

Statements (a), (c), and (d) are correct.

Step-by-step solution

Analyze statement (a)

One mole of any ideal gas at Normal Temperature and Pressure (NTP, 273.15 K and 1 atm) occupies a fixed volume of 22.4 liters. Therefore, one mole of \( \mathrm{CH}_{4} \) and one mole of \( \mathrm{NH}_{3} \), regardless of their masses, will occupy the same volume at NTP. However, 17 g of \( \mathrm{NH}_{3} \) is equivalent to one mole since the molar mass of \( \mathrm{NH}_{3} \) is approximately 17 g/mol, so this part of the statement is true.

Evaluate statement (b)

The statement claims that one gram mole of silver is \( \frac{108}{6.023 \times 10^{25}} \). This is incorrect. Molar mass of silver (Ag) is 108 g/mol. The quantity \( 6.023 \times 10^{23} \) represents Avogadro's number, which is the number of particles (atoms/molecules) in one mole, not grams per mole. Therefore, this statement is incorrect.

Check statement (c)

One gram mole of \( \mathrm{CO}_{2} \) implies one mole of \( \mathrm{CO}_{2} \), which is \( 6.023 \times 10^{23} \) molecules of \( \mathrm{CO}_{2} \). This entire mole is \( 6.023 \times 10^{23} \) times heavier than a single molecule of \( \mathrm{CO}_{2} \), which matches the definition and is correct.

Verify statement (d)

One mole of silver (Ag) has a molar mass of 108 g/mol, while calcium (Ca) has a molar mass of approximately 40 g/mol. Two moles of calcium would weigh \( 2 \times 40 = 80 \) g. Since 108 g of silver is more than 80 g, this statement is correct.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry and physics that helps to understand behavior of gases in different conditions. The formula is expressed as \( PV = nRT \), where:

• \( P \) represents pressure
• \( V \) is volume
• \( n \) is the number of moles
• \( R \) is the ideal gas constant
• \( T \) denotes temperature in Kelvin

At Normal Temperature and Pressure (NTP), which is 273.15 K and 1 atm, one mole of any ideal gas occupies a volume of 22.4 liters. This is a critical aspect of the Ideal Gas Law when analyzing gases under standard conditions. In the context of the exercise, both \( \mathrm{CH_4} \) and \( \mathrm{NH_3} \) as gases at NTP will occupy this same volume per mole, regardless of their actual mass. The law is useful since it simplifies the relationships between these variables, allowing calculations of unknown values when other info is available.

Avogadro's Number

Avogadro's Number is a key concept in chemistry, providing a bridge between the atomic world and macroscopic measurements. It is defined as \( 6.023 \times 10^{23} \), representing the number of atoms, ions, or molecules present in one mole of a substance. This constant is crucial because it allows chemists to count entities like molecules and atoms by weighing macroscopic amounts.
In practice, Avogadro's Number allows us to understand the scale and relationships in chemical reactions and properties. For instance, in the exercise, when discussing the weight of one gram mole of \( \mathrm{CO_2} \) or silver, Avogadro’s Number helps equate the familiar molar mass in labs to the more abstract number of particles. Thus, it performs an important function in converting between scale of individual atoms/molecules and laboratory-scale measurements.

Molar Mass Calculations

Molar mass is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). It is a useful measure because it links the mass of a sample to the number of moles it contains. To determine the molar mass, one sums the atomic masses of all the atoms present in a molecule. For example, the molar mass of \( \mathrm{NH_3} \) is calculated by adding the atomic masses of one nitrogen and three hydrogen atoms, approximating to 17 g/mol.
In exercises like the given example, molar mass calculations are critical for verifying the correctness of statements. Such computations help determine comparisons, such as whether one mole of silver has a greater or lesser mass than multiple moles of calcium. This ensures users understand weights and interactions of different substances, crucial for experimenting and practical laboratory applications.