Identify Alkaline Earth Metal: Oxide Reaction Problem

Hey guys! Let's dive into this interesting chemistry problem where we need to identify an alkaline earth metal based on the reaction of its oxide with water. This is a classic type of problem in chemistry, and understanding the steps to solve it can really boost your problem-solving skills. So, buckle up, and let’s get started!

Deciphering the Problem: The Oxide, Water, and Mass Percentage Puzzle

Okay, so the core of the problem lies in understanding the reaction between an alkaline earth metal oxide and water. We're given that 6.12 grams of this oxide reacts with 221.889 grams of water, and the resulting solution has a 3% mass fraction of the metal hydroxide. Our mission, should we choose to accept it (and we do!), is to figure out which alkaline earth metal we're dealing with. Is it magnesium (Mg), calcium (Ca), barium (Ba), or strontium (Sr)? This might sound like a daunting task, but don't worry, we'll break it down step by step.

The keywords here are alkaline earth metal oxide, reaction with water, mass percentage, and identifying the metal. These clues will guide us through the process. We need to understand how these oxides react with water, how to calculate molar masses, and how to use the given mass percentage to find the molar mass of the metal. Remember, chemistry is like solving a puzzle; each piece of information is crucial for completing the picture.

Laying the Foundation: Understanding the Chemistry

First things first, let's talk chemistry basics. Alkaline earth metals (Group 2 of the periodic table) readily react with oxygen to form oxides. These oxides, in turn, react with water to form hydroxides. This reaction is key to solving our problem. The general reaction can be represented as:

MO (s) + H₂O (l) → M(OH)₂ (aq)

Where:

• MO represents the alkaline earth metal oxide
• M(OH)₂ represents the alkaline earth metal hydroxide

Now, why is this important? Because the molar mass of the metal (M) is hidden within the molar mass of the metal hydroxide [M(OH)₂], which we can deduce from the given mass percentage. See where we're going with this? The mass percentage gives us a link to the compound formed, and the compound's molar mass can lead us to the metal itself. Think of it like following a breadcrumb trail!

Cracking the Code: Step-by-Step Solution

Alright, let's roll up our sleeves and tackle this problem head-on. Here's a step-by-step guide to solving this mystery:

Step 1: The Molar Mass Connection

Our ultimate goal is to find the molar mass of the metal (M). To get there, we need to relate the given mass percentage (3%) to the molar mass of the metal hydroxide [M(OH)₂]. Remember, the mass percentage tells us the proportion of the hydroxide in the solution.

The solution is formed by dissolving the metal oxide in water. So, the total mass of the solution is the sum of the mass of the oxide and the mass of the water:

Total mass of solution = Mass of oxide + Mass of water

Plugging in the given values:

Total mass of solution = 6.12 g + 221.889 g = 228.009 g

Now, we know that the mass percentage of the hydroxide in the solution is 3%. This means:

(Mass of M(OH)₂ / Total mass of solution) * 100% = 3%

We can rearrange this equation to find the mass of the hydroxide:

Mass of M(OH)₂ = (3% / 100%) * Total mass of solution

Mass of M(OH)₂ = 0.03 * 228.009 g = 6.84027 g

Step 2: Moles and the Magic Number

We've found the mass of the hydroxide. Now, let's convert this to moles. Remember, moles are a chemist's best friend! To do this, we need the molar mass of M(OH)₂. But wait, we don't know what M is yet! This is where we'll use a little algebraic magic.

Let's represent the molar mass of the metal (M) as 'x'. The molar mass of oxygen (O) is approximately 16 g/mol, and the molar mass of hydrogen (H) is approximately 1 g/mol. Therefore, the molar mass of M(OH)₂ can be expressed as:

Molar mass of M(OH)₂ = x + 2 * (16 + 1) = x + 34 g/mol

Now, we can calculate the number of moles of M(OH)₂:

Moles of M(OH)₂ = Mass of M(OH)₂ / Molar mass of M(OH)₂

Moles of M(OH)₂ = 6.84027 g / (x + 34 g/mol)

Step 3: Oxide to Hydroxide - The Mole Ratio

Here's a crucial step: The balanced chemical equation (MO (s) + H₂O (l) → M(OH)₂ (aq)) tells us that 1 mole of the metal oxide (MO) reacts to produce 1 mole of the metal hydroxide [M(OH)₂]. This is a 1:1 mole ratio.

So, the number of moles of MO that reacted is equal to the number of moles of M(OH)₂ formed. We already have an expression for the moles of M(OH)₂. Now, let's find an expression for the moles of MO.

Molar mass of MO = x + 16 g/mol (where 'x' is the molar mass of M)

Moles of MO = Mass of MO / Molar mass of MO

Moles of MO = 6.12 g / (x + 16 g/mol)

Since moles of MO = moles of M(OH)₂:

6. 12 g / (x + 16 g/mol) = 6.84027 g / (x + 34 g/mol)

Step 4: Solving for 'x' - The Algebraic Showdown

We've got an equation with one unknown ('x', the molar mass of the metal). It's time to unleash our algebraic skills and solve for 'x'. This might look a little intimidating, but hang in there!

Cross-multiplying the equation:

6. 12 g * (x + 34 g/mol) = 6.84027 g * (x + 16 g/mol)

Expanding both sides:

6. 12x + 208.08 = 6.84027x + 109.44432

Rearranging to isolate 'x':

6. 84027x - 6.12x = 208.08 - 109.44432

7. 72027x = 98.63568

Solving for 'x':

x = 98.63568 / 0.72027

x ≈ 136.94 g/mol

Step 5: The Grand Reveal - Identifying the Metal

We've found that the molar mass of the metal (M) is approximately 136.94 g/mol. Now, we need to compare this value to the molar masses of the alkaline earth metals given in the options:

• Magnesium (Mg): ~24 g/mol
• Calcium (Ca): ~40 g/mol
• Barium (Ba): ~137 g/mol
• Strontium (Sr): ~88 g/mol

Comparing our calculated molar mass (136.94 g/mol) with the options, it's clear that the metal is Barium (Ba)! We've cracked the case!

Key Takeaways and Pro Tips

• Understanding the Chemistry: This problem highlights the importance of understanding the reactions between metal oxides and water. Knowing the balanced chemical equation is crucial.
• Molar Mass is Your Friend: Molar mass is the key to connecting mass and moles, which are fundamental in stoichiometry problems.
• Mass Percentage Magic: Mass percentage provides a link between the mass of a component and the total mass of the solution. Master this concept!
• Step-by-Step Approach: Break down complex problems into smaller, manageable steps. This makes the process less overwhelming and reduces the chances of errors.
• Algebraic Confidence: Don't shy away from algebra! Practice solving equations, as it's a vital skill in chemistry.

Practice Makes Perfect

To truly master this type of problem, practice, practice, practice! Try solving similar problems with different alkaline earth metals and varying mass percentages. You can even create your own problems to challenge yourself. The more you practice, the more comfortable you'll become with the concepts and the problem-solving process.

So there you have it, guys! We've successfully identified the alkaline earth metal in this tricky problem. Remember, chemistry is all about understanding the relationships between different concepts and applying them systematically. Keep practicing, keep exploring, and you'll become a chemistry whiz in no time!