Question

Determine the number of chloride ions in 10.75 g of magnesium chloride.

Short answer

There are approximately \(1.36 \times 10^{23}\) chloride ions in 10.75 g of magnesium chloride.

Step-by-step solution

Find the molar mass of magnesium chloride (MgCl2)

To determine the moles of MgCl2, we need to know its molar mass. The molar mass of a compound can be calculated by adding the molar masses of all its atoms. In this case, we have one magnesium atom (Mg) and two chloride atoms (Cl). The molar masses of Mg and Cl are approximately 24.31 g/mol and 35.45 g/mol, respectively. So, the molar mass of MgCl2 = (24.31 g/mol) + 2 * (35.45 g/mol) = 24.31 g/mol + 70.9 g/mol = 95.21 g/mol.

Find the moles of magnesium chloride (MgCl2)

To determine the moles of magnesium chloride present in 10.75 g, we use the formula: moles of MgCl2 = (mass of MgCl2) / (molar mass of MgCl2) moles of MgCl2 = 10.75 g / 95.21 g/mol ≈ 0.113 moles

Determine the moles of chloride ions (Cl-)

In magnesium chloride (MgCl2), there are two chloride ions for every magnesium ion. Therefore, for each mole of MgCl2, there will be two moles of Cl- ions. moles of Cl- ions = 2 * moles of MgCl2 = 2 * 0.113 moles ≈ 0.226 moles

Calculate the number of chloride ions

To calculate the number of chloride ions, we need to use Avogadro's constant, which states that there are approximately 6.022 x 10^23 particles (atoms, ions, or molecules) per mole. Number of chloride ions = moles of Cl- ions * Avogadro's constant Number of chloride ions = 0.226 moles * 6.022 x 10^23 ions/mol ≈ 1.36 x 10^23 ions So, there are approximately \(1.36 \times 10^{23}\) chloride ions in 10.75 g of magnesium chloride.

Key concepts

The Mole Concept

Understanding the mole concept is essential for studying chemistry. The mole is a fundamental unit in chemistry that signifies a specific quantity - much like a 'dozen' refers to 12 items, a mole refers to approximately 6.022 x 10^23 of anything. This number, known as Avogadro's number, represents the number of particles (atoms, molecules, ions, electrons) in one mole of a substance.

The beauty of using moles lies in its ability to provide a bridge between the microscopic world of atoms and molecules and the macroscopic world we experience daily. It allows chemists to count out particles by weighing them, which is far more practical than counting each particle by hand.

For example, if you have a mole of magnesium chloride (MgCl2), you possess 6.022 x 10^23 formula units of that compound. This is why understanding the mole concept helps in solving the exercise of determining the number of chloride ions in a given mass of magnesium chloride.

Avogadro's Number

Avogadro's number, 6.022 x 10^23, is more than just a gigantic quantity; it's a constant that links the subatomic scale to our macro-scale measurements. For chemists and students learning about chemical quantities, Avogadro's number serves as a key conversion factor.

The use of Avogadro's number falls under what's called the mole concept. When you express an amount of substance in moles, you're relating a mass of your sample to the number of particles it contains. This is especially powerful because it takes the guesswork out of dealing with immense numbers of tiny particles.

By using Avogadro's number in the step-by-step solution to find the number of chloride ions from the moles of magnesium chloride, the abstract becomes concrete, and the invisible world of atoms and molecules becomes quantifiable and therefore understandable.

Molar Mass

Molar mass is the weight of one mole of a substance and is expressed in grams per mole (g/mol). It's an intrinsic property of each element and compound, reflecting the combined mass of all the atoms within a molecule as if we're stacking them up on a scale. The molar mass is crucial for converting between grams and moles, enabling chemists to make precise calculations about quantities in reactions.

In the exercise, the molar mass of magnesium chloride is calculated by adding the molar masses of magnesium and chloride. Each atom or ion's molar mass is an average of all its isotopes' masses, taking into account their natural abundance. Knowing the molar mass of magnesium chloride allows us to work backward from a certain mass to determine the number of moles present, which is the first step in calculating the number of chloride ions. This illustrates the importance of molar mass in solving chemistry problems.