Problem 94 - Chemistry and Chemical Reactivity

Question

Elemental sulfur \((1.256 \mathrm{g})\) is combined with fluorine, \(\mathrm{F}_{2},\) to give a compound with the formula \(\mathrm{SF}_{x},\) a very stable, colorless gas. If you have isolated \(5.722 \mathrm{g}\) of \(\mathrm{SF}_{x}\) what is the value of \(x ?\)

Step-by-Step Solution

Answer

The value of x is 6.

Step 1: Determine the Moles of Sulfur

First, calculate the moles of elemental sulfur (S) using its atomic mass. The atomic mass of S is approximately 32.07 g/mol. The formula to calculate moles is: \[ \text{moles of S} = \frac{\text{mass of S}}{\text{molar mass of S}} \]Substituting the given values:\[ \text{moles of S} = \frac{1.256}{32.07} = 0.03917 \text{ moles} \]

Step 2: Calculate the Moles of SF_x

Next, calculate the moles of the compound SF_x using its mass. Since we have isolated 5.722 g of SF_x, we need to find its molar mass in terms of x (M_SF_x).The formula for molar mass (M_SF_x) is:\[ \text{Molar mass of SF}_x = 32.07 + x(18.998) \]The number of moles of SF_x is:\[ \text{moles of SF}_x = \frac{5.722}{M_{SF_x}} \]

Step 3: Setting up and Solving the Equation

Since the moles of sulfur in S must equal the moles of sulfur in SF_x, equate the two moles:\[ 0.03917 = \frac{5.722}{32.07 + 18.998x} \]Rearrange this equation to solve for x:\[ 0.03917(32.07 + 18.998x) = 5.722 \]\[ 1.2572499 + 0.74448626x = 5.722 \]\[ 0.74448626x = 4.46475 \]\[ x = \frac{4.46475}{0.74448626} \approx 6 \]

Step 4: Verify the Result

Verify the calculation by plugging the value of x back into the formula for moles of SF_x and checking that it matches the initial moles of sulfur.\[ \text{molar mass of SF}_6 = 32.07 + 6(18.998) = 146.058 \]\[ \text{moles of SF}_6 = \frac{5.722}{146.058} \approx 0.03917 \text{ moles} \]The calculations confirm that when x = 6, the moles of SF_6 equals the moles of initial sulfur, validating our solution.

Key Concepts

Molecular Formula Determination

Determining the molecular formula of a compound involves figuring out the types and numbers of atoms present in a single molecule of the compound. In the given problem, we want to determine the value of \(x\) in the formula \(\text{SF}_x\). This means we are trying to find out how many fluorine atoms are bound to one sulfur atom. The process generally begins by examining the given mass of the original elements and the mass of the compound formed. In our case:- We start by calculating the number of moles of the elemental sulfur, which is given as 1.256 grams. Knowing sulfur's atomic mass (32.07 g/mol), we can find the moles of sulfur.- The moles of sulfur found are critical because they will exactly match the moles of sulfur present in \(\text{SF}_x\). By establishing a relationship between these moles and the mass of \(\text{SF}_x\), we can calculate the moles and subsequently the number of fluorine atoms \(x\) through simple algebra.Understanding the molecular formula often involves ensuring that every mole of an element in a reaction or a compound balances out perfectly with its moles elsewhere in the same or resulting material. Basically, this ensures that matter is neither created nor destroyed, following the law of conservation of mass.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, reflecting the sum of the masses of all atoms in a molecule. For our compound \(\text{SF}_x\), calculating the molar mass is crucial because it bridges the gap between mass and moles. The approach to calculating molar mass here involves:- Adding the molar mass of sulfur (32.07 g/mol) to \(x\) times the molar mass of fluorine (18.998 g/mol). Thus, the molar mass is given by \(32.07 + x(18.998)\).- Knowing the mass of the compound (5.722 g), we apply the formula for moles: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). This lets us equate the moles of \(\text{SF}_x\) to those of sulfur previously calculated, which isolates and helps determine \(x\).Accurate molar mass calculation is essential as it directly influences the values obtained in stoichiometric calculations. Reliable calculations of molar mass enable one to convert between the mass of a compound and the number of moles, maintaining the integrity of stoichiometric relationships.

Chemical Reaction Calculations

Chemical reaction calculations involve interpreting and managing the transfer and transformation of substances through chemical equations. In stoichiometry, the objective is to work out the quantities of reactants and products involved in chemical reactions.- By equating the moles of sulfur initially used to those found in \(\text{SF}_x\), we ensure that the quantities accounted for conform to stoichiometric principles.- This relates directly to the law of conservation of mass, asserting that mass is neither created nor destroyed. Each mole in reactants must have a corresponding mole in the products. - In our exercise, determining \(x\) gives insight into the precise stoichiometry of the reaction and thus what the exact formula of the stable gas \(\text{SF}_6\) is.It's critical to accurately perform these calculations since they help predict the outcomes of reactions. Whether you're scaling reactions for industrial purposes or completing them in a laboratory, understanding stoichiometry ensures proper use and conversion of materials, minimizing waste and optimizing yields.