Question

which of the following describes a saturated solution?
a. 30 grams of kno₃ dissolved in 100 grams of water at 15°c
b. 60 grams of nano₃ dissolved in 100 grams of water at 15°c
c. 30 grams of k₂cr₂o₇ dissolved in 100 grams of water at 50°c
d. 60 grams of nacl dissolved in 100 grams of water at 90°c

Explanation:

To determine a saturated solution, we need to recall the solubility values of each solute at the given temperatures.

Step1: Recall Solubility Data

• For \( \text{KNO}_3 \) at \( 15^\circ\text{C} \), solubility is about 25 g/100 g water. So 30 g would be supersaturated (not saturated yet? Wait, no—wait, maybe I mixed up. Wait, actually, solubility of \( \text{KNO}_3 \) at 15°C is ~25 g, so 30 g would be more than solubility, but wait, no—wait, maybe I made a mistake. Wait, let's check each:
• \( \text{NaNO}_3 \) at 15°C: solubility is about 85 g/100 g water. So 60 g is less than 85, so unsaturated.
• \( \text{K}_2\text{Cr}_2\text{O}_7 \) at 50°C: solubility is about 30 g/100 g water. So 30 g dissolved would be saturated (since it's equal to solubility).
• \( \text{NaCl} \) at 90°C: solubility is about 40 g/100 g water. 60 g is more than 40, but wait, no—wait, no, 60 g would be supersaturated? Wait, no, maybe I messed up. Wait, let's correct:

Wait, actual solubility values (approximate):

• \( \text{KNO}_3 \) at 15°C: ~25 g/100g H₂O. So 30 g is more than solubility, but is that saturated? Wait, no—saturated is when no more can dissolve. If you dissolve 30 g, but solubility is 25, then it's supersaturated (but maybe the question considers saturated as at or above? No, saturated is when the solution holds the maximum amount at that temp. So if solubility is 25, then 30 g would have undissolved solute, so saturated (with undissolved). But wait, let's check \( \text{K}_2\text{Cr}_2\text{O}_7 \) at 50°C: solubility is ~30 g/100g H₂O. So 30 g dissolved means it's saturated (exactly at solubility).
• \( \text{NaNO}_3 \) at 15°C: ~85 g/100g H₂O. 60 g is less, so unsaturated.
• \( \text{NaCl} \) at 90°C: ~40 g/100g H₂O. 60 g is more, so supersaturated (but maybe the question's options have C as correct). Wait, let's re-express:

Option C: 30 g \( \text{K}_2\text{Cr}_2\text{O}_7 \) in 100 g water at 50°C. Solubility of \( \text{K}_2\text{Cr}_2\text{O}_7 \) at 50°C is approximately 30 g/100 g water. So this is exactly saturated.
Option A: \( \text{KNO}_3 \) at 15°C: solubility ~25 g, so 30 g is more than solubility, so it's supersaturated (but maybe the question considers saturated as including supersaturated? No, saturated is when the solution is in equilibrium with undissolved solute, i.e., maximum dissolved. So if solubility is 25, then 30 g would have 5 g undissolved, so saturated. But \( \text{K}_2\text{Cr}_2\text{O}_7 \) at 50°C: 30 g is exactly solubility, so saturated.
Wait, maybe the intended answer is C, because 30 g is exactly the solubility at 50°C for \( \text{K}_2\text{Cr}_2\text{O}_7 \), so it's saturated.

Step2: Evaluate Each Option

• Option A: \( \text{KNO}_3 \) at 15°C: solubility ~25 g. 30 g > 25 g, so saturated (with undissolved), but let's check others.
• Option B: \( \text{NaNO}_3 \) at 15°C: solubility ~85 g. 60 g < 85 g, so unsaturated.
• Option C: \( \text{K}_2\text{Cr}_2\text{O}_7 \) at 50°C: solubility ~30 g. 30 g = solubility, so saturated.
• Option D: \( \text{NaCl} \) at 90°C: solubility ~40 g. 60 g > 40 g, so supersaturated (but maybe the question considers saturated as at or above, but 60 g is way above, so not saturated in the sense of exactly at solubility).

So the best answer is C, as 30 g is exactly the solubility at 50°C for \( \text{K}_2\text{Cr}_2\text{O}_7 \), making it saturated.

Answer:

C. 30 grams of \( \text{K}_2\text{Cr}_2\text{O}_7 \) dissolved in 100 grams of water at \( 50^\circ\text{C} \)