At [tex]$40^{\circ} C$[/tex], 100 g of water dissolved 104 g sodium nitrate. 250 g of water dissolved =?
Answer (2)
Set up a proportion: 104 100 = x 250 .
Cross-multiply: 100 x = 250 × 104 .
Solve for x : x = 100 250 × 104 .
Calculate x : x = 260 . The final answer is 260 g .
Explanation
Understanding the Problem We are given that at 4 0 ∘ C , 100 g of water can dissolve 104 g of sodium nitrate. We want to find out how much sodium nitrate 250 g of water can dissolve at the same temperature.
Setting up a Proportion Let x be the amount of sodium nitrate that 250 g of water can dissolve. We can set up a proportion to solve this problem. The proportion is: 104 g sodium nitrate 100 g water = x g sodium nitrate 250 g water .
Solving for x To solve for x , we can cross-multiply: 100 × x = 250 × 104 Now, divide both sides by 100: x = 100 250 × 104
Calculating the Amount of Sodium Nitrate Now, we calculate the value of x : x = 100 250 × 104 = 100 26000 = 260 So, 250 g of water can dissolve 260 g of sodium nitrate.
Final Answer Therefore, 250 g of water can dissolve 260 g of sodium nitrate at 4 0 ∘ C .
Examples
Understanding solubility is crucial in many real-world applications. For example, in the pharmaceutical industry, it's essential to know how much of a drug can dissolve in a solvent to create a stable and effective medication. Similarly, in the food industry, solubility affects the texture and stability of products like sugar in beverages or salt in soups. In environmental science, understanding the solubility of pollutants helps predict their movement and impact in water systems. Knowing that 100 g of water dissolves 104 g of sodium nitrate allows us to scale up and determine how much sodium nitrate dissolves in 250 g of water, which is a simple proportional relationship.
At 40°C, 250 g of water can dissolve 260 g of sodium nitrate. This is calculated using a proportion based on the solubility data for 100 g of water. The mathematical steps allow us to determine the amount of sodium nitrate in larger quantities of water.
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