Question

On a TGA, \(24.20 \mathrm{mg}\) of \(\mathrm{SrFeO}_{3}\), decomposed in a stream of hydrogen at \(700^{\circ} \mathrm{C}\) to give \(23.34 \mathrm{mg}\) of a mixture of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and SrO. Use these data to determine the value of \(x\).

Short answer

The value of \(x\) in the compound \(\mathrm{SrFeO}_{3-x}\) is 0.0389.

Step-by-step solution

Convert the given weights to moles

It's convenient to work with moles in stoichiometry rather than grams or milligrams. The molar mass of \(\mathrm{SrFeO}_3\), \(\mathrm{SrO}\), and \(\mathrm{Fe}_2\mathrm{O}_3\) are approximately 203.57 g/mol, 103.62 g/mol, and 159.69 g/mol respectively. So, the given weights convert to: \begin{align*} \mathrm{SrFeO}_3 &: 24.20 \, \mathrm{mg} = 24.20 / 203.57 = 0.1189 \, \mathrm{mol} \\ \mathrm{SrO + Fe}_2\mathrm{O}_3 &: 23.34 \, \mathrm{mg} = 23.34 / (103.62 + 1.5*159.69) = 0.0800 \, \mathrm{mol} \end{align*} The difference in mole amount before and after is \(0.1189 - 0.0800 = 0.0389 \, \mathrm{mol}\)

Determine the mass of the removed oxygen

This difference represents the oxygen atoms removed. It's known that the molar mass of the oxygen atom is approximately 16 g/mol. So, the removed oxygen weight is: \(0.0389 \, \mathrm{mol} \times 16 \, \mathrm{g/mol} = 0.6224 \, \mathrm{g}\)

Find the value of \(x\)

Now that the weight of the removed oxygen has been found, it is possible to calculate the value of \(x\). The weight of oxygen corresponds to the oxygen atoms in the \(\mathrm{SrFeO}_3\) molecule that have been removed. So, \(x\) can be calculated as follows: \(\frac{0.6224 \, \mathrm{g}}{16 \, \mathrm{g/mol}} = 0.0389 \, \mathrm{mol}\) Therefore, the value of \(x\) is 0.0389.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It follows the law of conservation of mass, stating that mass is neither created nor destroyed in a chemical reaction. This means the quantity of each element remains the same before and after the reaction, although they may be rearranged into different molecules.

By using stoichiometry, we calculate how much of a reactant is needed to produce a desired amount of product, or how much product is formed from a given amount of reactants. This involves balancing chemical equations and using the coefficients to compare the ratios of the amounts of each substance involved.

For instance, if we react substance A with substance B to form C, the balanced chemical equation can tell us how many moles of substance C are formed per mole of substance A reacted, allowing us to predict and measure substances with precision. It is a foundational skill in chemistry that helps to understand the detailed nature of reactions and is critical when conducting experiments or analyzing results, such as in the exercise with SrFeO3 decomposing into Fe2O3 and SrO.

Molar Mass Calculation

To calculate the molar mass of a compound, we sum the atomic masses of all atoms in a molecule. This is expressed in grams per mole (g/mol). It's a crucial step for stoichiometric calculations as it allows us to convert between the mass of a substance and the amount in moles, which is used for chemical reactions ratios due to Avogadro's principle.

For example, with SrFeO3, the molar mass is found by adding the atomic masses of one strontium (Sr), one iron (Fe), and three oxygen (O) atoms. If we have 24.20 mg of SrFeO3, we convert this mass to moles by dividing by the molar mass, which gives us the moles of SrFeO3 that will react.

Understanding the molar mass is essential for determining the stoichiometry of reactions, as seen in the exercise where it's necessary to perform a molar mass calculation for SrFeO3 and its decomposition products to find the value of x. Accurate molar mass calculations ensure precise measurements and chemical analyses in scientific processes.

Chemical Decomposition

Chemical decomposition is the process where a compound breaks down into two or more simpler substances. It is usually carried out through the application of heat, as seen in thermogravimetric analysis (TGA). TGA measures the amount of weight a substance loses as it decomposes when heated.

The importance of chemical decomposition lies in its ability to break complex molecules into simpler, more useful substances. For example, the decomposition of SrFeO3 into Fe2O3 and SrO may be used to separate and recover these components for other uses. The exercise provided demonstrates this by decomposing SrFeO3 in the presence of hydrogen to determine the stoichiometric value of x, which may represent the amount of oxygen released.

In practical applications, understanding the principles of decomposition helps in fields like materials science, where it's crucial for extracting metals from ores, among other uses. It's also an essential concept when analyzing the stability of substances under various conditions, such as temperature or pressure, which might influence the chemical composition and material properties.