Question

What percentage of the original \(\mathrm{Ag}^{+}\) remains in solution when \(175 \mathrm{mL} 0.0208 \mathrm{M} \mathrm{AgNO}_{3}\) is added to \(250 \mathrm{mL} 0.0380 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4} ?\)

Short answer

0% of the original Ag+ ions remain in the solution after the reaction is complete, because all react with CrO4-- ions.

Step-by-step solution

Determine stoichiometry of the reaction

The reaction between AgNO3 and K2CrO4 will form Ag2CrO4 and 2KNO3. The stoichiometric ratio implies it takes two molecules of AgNO3 to react with one molecule of K2CrO4 to form Ag2CrO4: \n2AgNO3 + K2CrO4 → Ag2CrO4 + 2KNO3

Calculate the number of moles

The number of moles of each reagent can be calculated using their concentration and the volume. Use the formula n = CV, where n is the numbers of moles, C is the concentration in mol/L and V is the volume in L. Convert mL to L (since 1L = 1000mL). Moles of Ag+ = 0.0208M * (175/1000)L = 0.00364 mol. Moles of CrO4-- = 0.0380M * (250/1000)L = 0.00950 mol.

Find the limiting reactant and Ag+ moles left out

The limiting reactant is the one that is completely consumed in the reaction. Based on the stoichiometry, 2 moles of Ag+ are required for each mole of CrO4--, so the limiting reactant is AgNO3. However, we have more Ag+ moles than required. The number of Ag+ moles left out = Total Ag+ moles - (2 * moles of CrO4--) = 0.00364 mol - 2 * 0.00950 mol = -0.01536 mol. This is a negative number, indicating all the CrO4-- ions can be completely consumed and also additional Ag+ can react. So, none of Ag+ ions will be left out. Percentage left out = (Ag+ moles left out/ Total AgNO3 moles) * 100 = 0.

Key concepts

Chemical Reaction Stoichiometry

Understanding chemical reaction stoichiometry is vital for correctly interpreting how substances relate to each other during a chemical reaction. It's all about the relative quantities and ratios in which reactants combine and products form.

Take the reaction from our exercise for example. The silver nitrate (AgNO3) reacts with potassium chromate (K2CrO4), producing silver chromate (Ag2CrO4) and potassium nitrate (KNO3). In simple terms, stoichiometry tells us that two moles of AgNO3 will react with one mole of K2CrO4. This ratio, 2:1, is the essence of stoichiometry in this scenario.

In more practical terms, if you're in a lab with a sample of K2CrO4, stoichiometry helps in determining how much AgNO3 you'll need to fully react with that sample – double, in this case. It prevents waste of chemicals and ensures the reaction can go to completion without any leftover reactants.

Limiting Reactant Calculation

The concept of the limiting reactant is crucial when dealing with chemical reactions. It limits the extent to which the chemical reaction can proceed and determines the amount of product formed.

In our exercise, we used stoichiometry to see that the limiting reactant was AgNO3, because it gets completely consumed before K2CrO4 runs out. Here's where a common misconception can occur: students might think more of a substance means it's the limiting reactant. However, it's actually about the stoichiometric ratios, not the initial amounts.

To calculate the limiting reactant, compare the mole ratio of the reactants to the ratio in the balanced equation. Once you identify the limiting reactant, it also becomes easy to calculate the maximum amount of product that can be formed, making this concept a cornerstone of quantitative chemistry.

Mole Concept

The mole concept is a fundamental building block of stoichiometry and allows us to count chemical entities (like atoms, molecules, or ions) using a quantity known as the mole, similar to a 'dozen' for eggs. One mole is Avogadro’s number (approximately 6.022 x 10^23) of particles.

For the exercise provided, we calculated the number of moles for AgNO3 and K2CrO4 using the formula n = CV. This calculation shows how many moles of each substance are present before the reaction takes place. Understanding the mole allows chemists to 'speak the same language' when measuring out reactants for a reaction and predicting product quantities. It's one reason why chemistry can be so precise in fields like pharmaceutical drug development where exact dosages are paramount.