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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?

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?
 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:
Amount of sugar in 250g of water=(204gsugar100gwater)×250gwater\text{Amount of sugar in 250g of water} = \left( \frac{204g \, \text{sugar}}{100g \, \text{water}} \right) \times 250g \, \text{water}

Now, calculate:

Amount of sugar in 250g of water=(204100)×250=2.04×250=510g\text{Amount of sugar in 250g of water} = \left( \frac{204}{100} \right) \times 250 = 2.04 \times 250 = 510g

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:
Increased solubility=510g+(0.30×510g)=510g+153g=663g\text{Increased solubility} = 510g + \left( 0.30 \times 510g \right) = 510g + 153g = 663g

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:

More sugar that can dissolve=663g510g=153g\text{More sugar that can dissolve} = 663g - 510g = 153g

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.

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