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\(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) solution of 1 molal concentration is present in 1 litre solution of \(2.684 \mathrm{~g} / \mathrm{cc} .\) How many moles of \(\mathrm{BaSO}_{4}\) would be precipitated on adding \(\mathrm{BaCl}_{2}\) in excess ? (a) 2 moles (b) 3 moles (c) 6 moles (d) 12 moles

Short Answer

Expert verified
3 moles of BaSO4 would be precipitated.

Step by step solution

01

Understanding the problem

First, understand that the task is to find out how many moles of BaSO4 would precipitate when excess BaCl2 is added to a 1 molal solution of Al2(SO4)3. Molality (m) is defined as moles of solute per kilogram of solvent. The density of the solution is given, which will help in finding the mass of the solvent.
02

Calculating the mass of the solvent

Use the density formula \(\text{density} = \frac{\text{mass}}{\text{volume}}\) to calculate the mass of the 1-liter (1000 cc) solution. Multiply the density (2.684 g/cc) with the volume (1000 cc) to get the mass of the solution: \(2.684\;\text{g/cc} \times 1000\;\text{cc} = 2684\;\text{g} \).
03

Calculating the mass of the solute

Since the solution has a molality of 1 molal, it contains 1 mole of Al2(SO4)3 per kilogram of solvent. The molar mass of Al2(SO4)3 is \(2(26.98) + 3(32.06) + 12(16.00)\) grams/mole. Calculate the mass of 1 mole of Al2(SO4)3 to determine how much mass of the solute is present.
04

Calculating the number of moles of SO4^2- in solution

Each mole of Al2(SO4)3 contains 3 moles of SO4^2-. Since there is 1 mole of Al2(SO4)3 in the solution, there are 3 moles of SO4^2- ions available to react with Ba^2+ ions from BaCl2.
05

Determining the theoretical yield of BaSO4 precipitation

BaCl2 is added in excess which means that all of the SO4^2- ions will react. According to the reaction stoichiometry, 1 mole of SO4^2- will react with 1 mole of Ba^2+ to form 1 mole of BaSO4. Hence, 3 moles of SO4^2- will precipitate as 3 moles of BaSO4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molality Calculation
When tackling chemistry problems, understanding units like molality is crucial. Molality (\( m \)) measures the concentration of a solution by indicating the number of moles of solute per kilogram of solvent. It鈥檚 different from molarity, which is moles per liter of solution. Here鈥檚 why molality is important: it remains unchanged with temperature, since mass doesn't vary like volume can with heat.

Let鈥檚 understand it with an example. Say we have a molality of 1 mol/kg. This means for every kilogram of solvent, there is 1 mole of solute dissolved. To find the molality, we need the mass of the solvent which can be calculated from the density (\( \frac{\text{mass}}{\text{volume}} \)), as seen in our exercise. If a solution has a density of 2.684 g/cm鲁, then 1 liter (which is 1000 cm鲁) of this solution would have a mass of 2.684 g/cm鲁 脳 1000 cm鲁 = 2684 g. To progress towards molality, we鈥檇 subtract the mass of the solute (calculated using its molar mass) from this total mass to get the mass of just the solvent.
Precipitation Reactions
Precipitation reactions are a staple in chemical reaction studies. In such a reaction, two soluble salts react to form one insoluble product, the 'precipitate', and another soluble salt. Being able to predict and understand these reactions is key to mastering many chemistry concepts.

In the context of our exercise, when we add an excess of BaCl鈧 to the Al鈧(SO鈧)鈧 solution, a reaction occurs where Ba虏鈦 ions from BaCl鈧 and SO鈧劼测伝 ions from Al鈧(SO鈧)鈧 form an insoluble salt, BaSO鈧, which precipitates out of the solution. The 'in excess' clue indicates that there will be more than enough Ba虏鈦 ions to react with every SO鈧劼测伝 ion available, ensuring complete precipitation.
Stoichiometry
Stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It鈥檚 a vital tool for predicting the outcomes of reactions and for understanding the quantitative relationships within them.

In the given problem, stoichiometry helps us figure out how many moles of BaSO鈧 will precipitate from the reaction between Al鈧(SO鈧)鈧 and excess BaCl鈧. Using the stoichiometric coefficients from the balanced equation (which, in our case, aren鈥檛 explicitly provided, but are implied to be 1:1 for SO鈧劼测伝 to Ba虏鈦), we find that 1 mole of SO鈧劼测伝 ions will react with 1 mole of Ba虏鈦 ions to form 1 mole of BaSO鈧. Since we have 3 moles of SO鈧劼测伝 from our 1 mole of Al鈧(SO鈧)鈧 (remember, each formula unit of Al鈧(SO鈧)鈧 has 3 sulfate ions), we鈥檒l form 3 moles of BaSO鈧 - answering our problem with option (b) 3 moles.

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Most popular questions from this chapter

The density of a \(56.0 \%\) by weight aqueous solution of 1 -propanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) is \(0.8975\) \(\mathrm{g} / \mathrm{cm}^{3}\). What is the mole fraction of the compound ? (a) \(0.292\) (b) \(0.227\) (c) \(0.241\) (d) \(0.276\)

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