Vitamin C Intake: Calculating Orange Juice Needed

Hey guys! Let's dive into a fun chemistry problem, specifically one involving vitamin C and orange juice! This is a classic example of how we can use chemistry to understand everyday things, like how much orange juice we need to drink to get our daily dose of vitamin C. This question is based on the UFJF-MG exam, which is a great way to challenge your knowledge. So, here's the deal: We're given that a yummy glass of orange juice has 400 ppm (parts per million) of vitamin C. This is a crucial piece of information. The problem then asks us: how many mL (milliliters) of orange juice does someone need to drink to hit their daily requirement of 60 mg (milligrams) of vitamin C? And we're also given that the density of the orange juice is 1.00 g/mL (grams per milliliter). Easy peasy, right? Alright, let's break this down step-by-step to make sure we get it right. Trust me, it's easier than you think when you know the steps! This is something that you can easily practice and get better at.

First, let's understand what 400 ppm means. This notation is super important in chemistry and helps us understand the concentration of a substance in a mixture. In this case, 400 ppm of vitamin C in the orange juice means that for every one million parts of orange juice, there are 400 parts of vitamin C. So, to make this easier to work with, we can translate this into a more useful unit. Let's convert this into milligrams of vitamin C per milliliter of orange juice. This is a common and useful conversion. If we consider one liter of orange juice (1000 mL), we can calculate the amount of vitamin C present. This involves using the density of the orange juice (1.00 g/mL). Remember, the density is key here, because it links mass and volume. Also, it’s worth noting that density is a very important concept in chemistry.

Now, let's walk through the steps together to figure out the final answer. We'll break it down as if we're working it out together. If you get lost, just re-read the part. Understanding units and conversions is the key to solving this. Let's start the breakdown.

Step-by-Step Solution

Convert ppm to mg/mL

Okay, let's convert those parts per million (ppm) into something more usable. We know 400 ppm means 400 parts of vitamin C per million parts of orange juice. Let's think about this in terms of mass, because we're dealing with milligrams (mg). First of all, remember that we can assume that 1 mL of orange juice has a mass of 1 g (because the density is 1.00 g/mL). And for 1 liter (1000 mL) of orange juice we have 1000 g.

• Convert ppm to g/mL: 400 ppm means 400 mg of vitamin C per liter of orange juice. We can rewrite the concentration in g/L as follows: (400 mg vitamin C / 1 L orange juice). Convert the milligrams into grams by dividing it by 1000 (1 g = 1000 mg), so we get 0.4 g/L. This tells us there are 0.4 grams of vitamin C in 1 liter of orange juice.
• Convert g/L to g/mL: We know 1 L is equal to 1000 mL. So, 0.4 g/L is the same as 0.4 g / 1000 mL = 0.0004 g/mL. This tells us there are 0.0004 grams of vitamin C in every milliliter of orange juice.
• Convert g/mL to mg/mL: Multiply by 1000 to convert grams to milligrams: 0.0004 g/mL * 1000 = 0.4 mg/mL. This is super helpful! We now know that the orange juice has 0.4 mg of vitamin C in every 1 mL. We're getting closer!

Calculate the Volume of Juice Needed

Alright, now that we know how much vitamin C is in each mL of orange juice (0.4 mg/mL), we can figure out how much juice someone needs to drink to get 60 mg of vitamin C. This is easy, and it is just a matter of proportion. Let's think through this step by step. You might find that it's useful to do it this way rather than the way you used to.

• Set up the equation: We want to find the volume (V) of orange juice needed. We know that in 1 mL, there is 0.4 mg of vitamin C. And we want 60 mg. Therefore, we can set up the proportion: (0.4 mg vitamin C / 1 mL orange juice) = (60 mg vitamin C / V mL orange juice).
• Solve for V: You can rearrange this equation to solve for V. The math gives you V = (60 mg * 1 mL) / 0.4 mg.
• Calculate: Doing the math, you will get V = 150 mL.

So, according to our calculations, a person needs to drink 150 mL of orange juice to get their 60 mg of daily vitamin C. That's it! We have solved this question!

Answer and Conclusion

Therefore, the correct answer is (B) 150 mL. Great job, guys! This problem illustrates a great chemistry problem in a way that is easily understandable. And we used ppm to mg/mL conversions to get there. Remember, these types of problems are pretty common in chemistry, and the key is to break them down step by step and pay close attention to your units. And now you've got it.

This is a good reminder of how important it is to have some understanding of chemistry in everyday life. Keep in mind that converting between units is one of the most important skills in chemistry. It can be applied in many other areas, like medicine, engineering, and environmental science. Also, keep practicing these types of problems, and you'll get better and better at them. You got this, and keep up the great work! Always remember that you can always re-read and work through the problem multiple times. This way, you can easily digest the process and improve.

• Key Takeaways:

  • Understanding ppm and its conversion to useful units like mg/mL.
  • Using density to relate mass and volume.
  • Applying proportional reasoning to solve for unknown quantities.

• Tips for Success:

  • Always write down your units and track them throughout your calculations. This helps prevent mistakes and makes it easier to spot errors.
  • Practice converting between different units of measurement.
  • Break down complex problems into smaller, more manageable steps.
  • If you're unsure, go back and review the definitions and concepts. This will help you a lot in the future. Don't be afraid to ask for help!

Hopefully, this detailed walkthrough helps you ace these types of problems in the future. Now go enjoy a glass of orange juice (in moderation, of course)!