Question

A 2.077 -g sample of an element, which has an atomic mass between 40 and \(55,\) reacts with oxygen to form 3.708 g of an oxide. Determine the formula of the oxide (and identify the element).

Short answer

First, calculate the moles of the unknown element using the average atomic mass: \(moles = \frac{2.077\,\text{g}}{47.5\,\text{g/mol}}\). Next, find the mass and moles of oxygen: \(mass = 3.708\,\text{g} - 2.077\,\text{g}\) and \(moles = \frac{mass}{16\,\text{g/mol}}\). Determine the mole ratio between the unknown element and oxygen by dividing their moles. Round the mole ratio to the nearest whole number to obtain the oxide's empirical formula. Finally, use the empirical formula and average atomic mass to identify the unknown element by comparing its calculated atomic mass to the periodic table.

Step-by-step solution

Calculate the moles of the element

First, we are given the mass of the element (2.077 g) and a range for its atomic mass (between 40 and 55). To make the calculations, we will use the average atomic mass of the range, which is 47.5. Recall that the number of moles can be found using the formula: moles = mass / molar_mass So, using the average atomic mass, moles of element = 2.077 g / 47.5 g/mol Calculate the moles of the element.

Calculate the moles of oxygen

To find the moles of oxygen, we first need to determine the mass of oxygen that reacted. We can do this by subtracting the mass of the element from the total mass of the oxide: Mass of oxygen = Total mass of oxide - Mass of element Mass of oxygen = 3.708 g - 2.077 g Calculate the mass of oxygen. Next, we need to find the moles of oxygen. The molar mass of oxygen is 16 g/mol. Using the formula from step 1: moles of oxygen = mass of oxygen / molar_mass of oxygen Calculate the moles of oxygen.

Determine the mole ratio

To find the empirical formula, we need to determine the mole ratio between the element and oxygen. We do this by dividing the moles of each element by the smaller number of moles: mole ratio = moles of element / moles of oxygen Calculate the mole ratio.

Round the mole ratio to the nearest whole number

In some cases, the mole ratio might not be a whole number. In this case, round the mole ratio to the nearest whole number to find the empirical formula of the compound (e.g., if the mole ratio is 1.5, the empirical formula would be Element2O3). Round the mole ratio and write the empirical formula of the oxide.

Identify the element

Finally, we can use the empirical formula to identify the element. Using the average atomic mass (47.5) and the empirical formula, divide the mass of the element by the number of atoms of the element in the formula. This should give us a value close to the actual atomic mass of the element, which can then be compared to the periodic table to identify the element. Identify the element by comparing the calculated atomic mass to the periodic table. You have now determined the formula of the oxide and identified the unknown element.

Key concepts

Moles Calculation

Understanding moles is essential in chemistry because it helps us count atoms and molecules in a given sample. A mole is a unit that represents Avogadro's number, approximately \(6.022 \times 10^{23}\), of particles, atoms, or molecules. When calculating moles, you can use the formula:

• \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \)

To illustrate, in the provided exercise, the mass of the element is given as 2.077 g, and we assume an average atomic mass of 47.5 g/mol. By plugging these values into the formula, we calculate the moles of the unknown element:\[ \text{moles of element} = \frac{2.077 \text{ g}}{47.5 \text{ g/mol}} \]This calculation is fundamental in understanding the composition of substances and allows further computation in this exercise, such as finding the mole ratio needed to determine the empirical formula.

Empirical Formula

An empirical formula depicts the simplest whole-number ratio of atoms in a compound. It is derived from the mole ratio of the elements within the compound. In the context of the exercise, after computing the moles of both the unknown element and oxygen, we determine their mole ratio.First, calculate the moles of oxygen:- Subtract the mass of the element (2.077 g) from the total mass of the oxide (3.708 g) to obtain the mass of oxygen: \[ \text{mass of oxygen} = 3.708 \text{ g} - 2.077 \text{ g} \]- Use the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), with the molar mass of oxygen being 16 g/mol, to find the moles of oxygen.Now, determine the mole ratio:- Divide the moles of each element by the smallest number of moles computed to obtain a ratio:\[ \text{mole ratio} = \frac{\text{moles of element}}{\text{moles of oxygen}} \]Finally, round the ratio to the nearest whole number to get the empirical formula. This formula helps understand the basic composition of the compound made from the element and oxygen.

Atomic Mass Identification

Atomic mass identification is crucial to determine the identity of unknown elements. The atomic mass is typically an element's average mass based on its isotopic distribution. By comparing the calculated atomic mass of an element from experimental data to known atomic masses from the periodic table, we can pinpoint the element's identity. In the exercise, you obtained an average atomic mass of 47.5 g/mol for calculations, knowing the elemental mass range from 40 to 55 g/mol. Once the empirical formula is acquired, you divide the component's atomic mass by the number of atoms of that element from the empirical formula. Look for a number close to the calculated atomic mass in the periodic table. This method provides a starting point to further hypothesize about the element's identity, ensuring that the assumptions made fit the broader context of established chemical knowledge. This step serves as a key application in identifying what element reacts to form the particular oxide described in chemical reaction experiments.