Question

Complete the table \begin{tabular}{llll} Substance & Mass & Moles & Number of Particles (atoms or molecules) \\ \(\mathrm{Ar}\) & \(-\) & \(4.5 \times 10^{-4}\) & \(-\) \\ \(\mathrm{NO}_{2}\) & \(-\) & \(-\) & \(1.09 \times 10^{20}\) \\ \(\mathrm{~K}\) & \(22.4 \mathrm{mg}\) & \(-\) & \(-\) \\ \(\mathrm{C}_{\mathrm{B} \mathrm{H}_{\mathrm{As}}}\) & \(3.76 \mathrm{~kg}\) & \(-\) & \(-\) \\ \hline \end{tabular}

Short answer

Mass (Ar) = 17.98 g, Moles (NO2) = 1.81 x 10^-19 mol, Mass (NO2) = 0.076 g, Moles (K) = 0.000573 mol, Number of particles (K) = 3.45 x 10^20, Moles (C_{B}H_{As}) and Number of particles (C_{B}H_{As}) cannot be determined without the number of B and As atoms.

Step-by-step solution

Find the molar mass of Argon (Ar)

To calculate the mass of Argon, first find its molar mass using the periodic table. The molar mass of Argon is approximately 39.95 g/mol.

Calculate the mass of Argon (Ar)

Use the molar mass and the number of moles of Argon to find the mass: Mass (Ar) = Moles (Ar) x Molar mass (Ar). Substitute the given value to obtain the mass.

Calculate the moles of Nitrogen Dioxide (NO2)

Use Avogadro's number, which states that 1 mole of any substance contains approximately 6.022 x 10^23 particles. Moles (NO2) = Number of particles (NO2) / Avogadro's number.

Calculate the mass of Nitrogen Dioxide (NO2)

Find the molar mass of NO2 (1 nitrogen atom's mass + 2 oxygen atoms' mass). Then, calculate the mass: Mass (NO2) = Moles (NO2) x Molar mass (NO2).

Calculate the moles of Potassium (K)

Convert the mass of Potassium from mg to g. Then, find the number of moles using its molar mass (approximately 39.10 g/mol): Moles (K) = Mass (K) in grams / Molar mass (K).

Calculate the number of Potassium (K) particles

Multiply the number of moles of Potassium by Avogadro's number to get the number of particles: Number of particles (K) = Moles (K) x Avogadro's number.

Calculate the moles of substance \(C_{B}H_{As}\)

First determine the molar mass based on the unspecified numbers of atoms B and As (we'll assume Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.01 g/mol, Arsenic (As) = 74.92 g/mol). Then, calculate the moles of the substance: Moles = Mass in grams / Molar mass.

Calculate the number of particles of \(C_{B}H_{As}\)

Use Avogadro's number to find the number of particles: Number of particles = Moles x Avogadro's number. Since we don't have the specific numbers for B and As, this calculation can only be done with those values.

Key concepts

Molar Mass

The molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance. It's expressed in grams per mole (g/mol) and can be found by summing the atomic masses of all atoms in a molecule, as listed on the periodic table. For example, water (H₂O) has a molar mass of approximately 18.02 g/mol, because it has two hydrogen atoms (each about 1.01 g/mol) and one oxygen atom (about 16.00 g/mol).

Understanding molar mass is crucial when converting between mass and moles, and it forms the basis for stoichiometric calculations in chemical reactions.

Avogadro's Number

Avogadro's number is one of the cornerstones of the mole concept in chemistry. It is defined as the number of particles (which could be atoms, molecules, ions, or electrons) in one mole of substance, and the value is approximately 6.022 x 10²³. This constant allows chemists to relate the macroscopic world of grams and liters to the microscopic world of atoms and molecules. When you're calculating the number of particles in a sample, you take the number of moles and multiply it by Avogadro's number. Similarly, if you have the number of particles and want to find the moles, you would divide by Avogadro's number.

Chemistry Stoichiometry

Chemistry stoichiometry refers to the quantitative relationships between reactants and products in a chemical reaction. It is the tool that allows chemists to predict the amounts of substances consumed and produced in a given reaction. Stoichiometry relies on balanced chemical equations and the principles of conservation of mass and charge. The coefficients in a balanced equation tell us the ratio between the numbers of moles of each substance. Stoichiometry is essential for calculating reactant and product quantities, whether you are dealing with mass, volume, number of particles, or energy changes in a reaction.

Converting Mass to Moles

To convert the mass of a substance to moles, you divide the mass by the molar mass of the substance. This step is a frequent starting point in stoichiometric calculations and allows chemists to move from the tangible world of mass to the concept of moles, which represents the amount of substance. For instance, if you have 10 grams of sodium chloride (NaCl), with a molar mass of about 58.44 g/mol, the number of moles of NaCl in your sample would be approximately 0.171 moles. This conversion is essential when interpreting chemical formulas and equations, as these are typically expressed in terms of moles.

Calculating Number of Particles

After determining the number of moles of a substance, you can calculate the number of particles present using Avogadro's number. To do this, you multiply the number of moles by 6.022 x 10²³ particles/mole. This calculation is helpful when you need to understand the quantity of a substance at the microscopic level. For example, if you have 0.2 moles of a compound, it contains 0.2 x 6.022 x 10²³, or approximately 1.20 x 10²³, particles. This is fundamental when dealing with reaction mechanisms, material properties, and nanotechnology applications.