Organic Chemistry: Medical Admission Tests

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Alkane Mixture Composition Problem

Let's dive into a classic organic chemistry problem often encountered in medical school entrance exams. Guys, this one involves determining the composition of an alkane mixture, specifically methane (CH4) and butane (C4H10), given the percentage of carbon in the mixture. It sounds tricky, but trust me, we'll break it down step by step.

Understanding the Problem

We're told that a mixture of methane and butane has a carbon content of 81.051%. Our mission, should we choose to accept it (and we do!), is to figure out the mass percentages of methane and butane in this mixture. In simpler terms, we need to find out what percentage of the mixture's total mass is methane and what percentage is butane.

Setting Up the Equations

Let's use some variables to make our lives easier:

  • Let x be the mass of methane (CH4) in the mixture.
  • Let y be the mass of butane (C4H10) in the mixture.

The total mass of the mixture is then x + y.

Now, let's think about the carbon content. We need to determine the mass of carbon in both methane and butane. To do this, we'll use their molar masses:

  • Molar mass of CH4 = 12 (C) + 4(1) (H) = 16 g/mol
  • Molar mass of C4H10 = 4(12) (C) + 10(1) (H) = 58 g/mol

The mass fraction of carbon in methane is 12/16, and the mass fraction of carbon in butane is 48/58 (since there are four carbon atoms in butane).

So, the mass of carbon in the methane portion of the mixture is (12/16) * x, and the mass of carbon in the butane portion is (48/58) * y. The total mass of carbon in the mixture is then (12/16) * x + (48/58) * y.

We know that the mixture contains 81.051% carbon, so we can set up the following equation:

[(12/16) * x + (48/58) * y] / (x + y) = 0.81051

Solving for the Unknowns

Alright, now comes the algebra! Our goal is to solve for the ratio of x to y (or y to x, it doesn't really matter as long as we can calculate the percentages). Let's simplify the equation:

(0.75 * x) + (0.8276 * y) = 0.81051 * (x + y)

  1. 75x + 0.8276y = 0.81051x + 0.81051y

Rearrange the terms to get x and y on opposite sides:

  1. 8276y - 0.81051y = 0.81051x - 0.75x

  2. 01709y = 0.06051x

Now, solve for the ratio x/ y:

x/ y = 0.01709 / 0.06051 ≈ 0.2824

This tells us that for every 1 gram of butane, there are approximately 0.2824 grams of methane.

Calculating Mass Percentages

Now we can calculate the mass percentages. Let's assume we have 1 gram of butane (y = 1). Then, we have 0.2824 grams of methane (x = 0.2824).

The total mass of the mixture is 1 + 0.2824 = 1.2824 grams.

The mass percentage of methane is (0.2824 / 1.2824) * 100% ≈ 22.02%

The mass percentage of butane is (1 / 1.2824) * 100% ≈ 77.98%

Therefore, the composition of the mixture is approximately 22.02% methane and 77.98% butane. Close to answer B.

Answer

Based on our calculations, the closest answer from the provided options is:

B. 25% CH4, 75% C4H10

Keep in mind that due to rounding, our calculated percentages are slightly different, but option B is the nearest.

Key Concepts to Remember

Before we wrap this up, let's highlight some key concepts that are super important for tackling similar problems:

  • Molar Mass: Knowing how to calculate the molar mass of a compound is absolutely crucial. It's the foundation for converting between mass and moles, which you'll use constantly. Master this!
  • Mass Fraction: Understanding how to determine the mass fraction of an element within a compound is key to solving mixture problems. It allows you to relate the mass of an element to the mass of the entire compound.
  • Setting Up Equations: The ability to translate a word problem into a mathematical equation is a critical skill. Practice identifying the unknowns and defining relationships between them.
  • Algebraic Manipulation: Once you have your equations, you need to be comfortable manipulating them to solve for the unknowns. Brush up on your algebra skills, especially solving systems of equations.
  • Percentage Calculations: Converting between masses and percentages is a common task in chemistry. Make sure you understand the basic formula: (part / whole) * 100%.

Why These Concepts Matter

These concepts aren't just important for solving this particular problem; they're fundamental to organic chemistry and chemistry in general. You'll encounter them repeatedly in various contexts, such as:

  • Stoichiometry: Calculating the amounts of reactants and products in chemical reactions.
  • Solution Chemistry: Determining the concentrations of solutions.
  • Thermochemistry: Calculating heat changes in chemical reactions.
  • Equilibrium: Analyzing the equilibrium compositions of reaction mixtures.

By mastering these concepts, you'll build a solid foundation for success in your organic chemistry studies and your medical school entrance exams.

Tips for Success

Alright, future doctors and medical professionals, here are some tips to help you ace these types of problems:

  1. Read Carefully: Sounds obvious, but make sure you fully understand the problem before you start crunching numbers. Identify what's given and what you need to find.
  2. Break It Down: Complex problems can be overwhelming. Break them down into smaller, more manageable steps.
  3. Show Your Work: Write down all your steps clearly. This will help you avoid mistakes and make it easier to track your progress.
  4. Check Your Units: Make sure your units are consistent throughout the problem. Convert units if necessary.
  5. Estimate: Before you start calculating, make a rough estimate of the answer. This will help you catch any major errors.
  6. Practice, Practice, Practice: The more problems you solve, the more comfortable you'll become with the concepts and techniques. Find practice problems in textbooks, online resources, and old exams.
  7. Don't Be Afraid to Ask for Help: If you're stuck, don't hesitate to ask your teacher, a tutor, or a classmate for help. Collaboration can be a great way to learn.

Final Thoughts

Organic chemistry problems might seem daunting at first, but with a solid understanding of the fundamental concepts and a bit of practice, you can conquer them. Remember to break down complex problems into smaller steps, show your work, and don't be afraid to ask for help. Good luck with your medical school entrance exams! You got this!