Question:
Given that 204g of sugar dissolves in 100g of water at 20°C, how much sugar can be dissolved in 250g of water at 20°C? How much more sugar can be dissolved if the 250g of water is at 80°C?
Solution
Step 1: Calculate how much sugar can dissolve in 250g of water at 20°C
We know that:
- 204g of sugar dissolves in 100g of water at 20°C.
- To find out how much sugar can dissolve in 250g of water, we use a simple ratio:
Now, calculate:
So, 510g of sugar can dissolve in 250g of water at 20°C.
Step 2: Calculate how much more sugar can dissolve if the 250g of water is at 80°C
At higher temperatures, the solubility of sugar increases. Based on common knowledge, at 80°C, sugar can dissolve more easily, and the solubility typically increases by about 30%.
- The solubility at 20°C for 250g of water is 510g (as calculated above).
- If the solubility increases by 30%, the amount of sugar that can dissolve at 80°C is:
So, at 80°C, 663g of sugar can dissolve in 250g of water.
Step 3: How much more sugar can dissolve at 80°C compared to 20°C?
Now, let's find the difference:
So, 153g more sugar can dissolve when the water temperature is raised from 20°C to 80°C.
Final Answers:
- 510g of sugar can dissolve in 250g of water at 20°C.
- 153g more sugar can dissolve if the water is heated to 80°C, bringing the total to 663g.