What is the smallest volume of water at 20c that could be used to dissolve and remove potassium nitrate impurities and leave pure sodium hydrogen carbonate?
To calculate the smallest volume of water needed to dissolve and remove potassium nitrate impurities and leave pure sodium hydrogen carbonate, we need to consider the solubility of both compounds.
1. Determine the solubility of potassium nitrate (KNO3) and sodium hydrogen carbonate (NaHCO3) at 20°C:
- The solubility of potassium nitrate is approximately 31.6 g/100 mL of water at 20°C.
- The solubility of sodium hydrogen carbonate is approximately 7.8 g/100 mL of water at 20°C.
2. Calculate the amount of potassium nitrate impurities that need to be dissolved and removed:
- Assume we have a known amount of impure sodium hydrogen carbonate and we need to remove all the potassium nitrate impurities completely.
- Suppose the impure sodium hydrogen carbonate weighs "x" grams.
- The amount of potassium nitrate impurities can vary, but we'll consider the worst-case scenario where the impurities weigh the same as the sodium hydrogen carbonate (x grams).
3. Determine the amount of water required to dissolve the maximum amount of potassium nitrate impurities:
- To completely dissolve the potassium nitrate impurities, we need to use the solubility value mentioned earlier.
- Since potassium nitrate has a solubility of 31.6 g/100 mL of water, we need to dissolve "x" grams of potassium nitrate.
- So, the volume of water required can be calculated using the formula: (x g of potassium nitrate) / (31.6 g/100 mL) = (x/31.6) * 100 mL
4. Calculate the remaining volume of water needed to dissolve the sodium hydrogen carbonate:
- After dissolving the potassium nitrate impurities, we need to dissolve the remaining amount of sodium hydrogen carbonate.
- Assume the remaining sodium hydrogen carbonate weighs "y" grams (pure sodium hydrogen carbonate).
- The solubility of sodium hydrogen carbonate is given as 7.8 g/100 mL of water.
- So, the volume of water required to dissolve "y" grams of sodium hydrogen carbonate can be calculated using the formula: (y g of sodium hydrogen carbonate) / (7.8 g/100 mL) = (y/7.8) * 100 mL
5. Add the two volumes of water calculated in steps 3 and 4 to get the total volume needed:
Total volume of water = (x/31.6) * 100 mL + (y/7.8) * 100 mL
Note: The actual volume of water needed may vary depending on the exact weight of impurities and sodium hydrogen carbonate.
To determine the smallest volume of water needed to dissolve and remove potassium nitrate impurities while leaving pure sodium hydrogen carbonate, you need to understand the solubility of these compounds and their solubility product constants.
1. Solubility of Potassium Nitrate (KNO3):
Potassium nitrate is a highly soluble compound in water. At 20°C, the solubility of potassium nitrate is approximately 31 grams per 100 ml of water.
2. Solubility of Sodium Hydrogen Carbonate (NaHCO3):
Sodium hydrogen carbonate, also known as baking soda, is also a soluble compound in water. At 20°C, the solubility of sodium hydrogen carbonate is approximately 7.8 grams per 100 ml of water.
To calculate the smallest volume of water required, we can assume that the maximum amount of potassium nitrate will dissolve while keeping all sodium hydrogen carbonate dissolved.
Since the solubility of potassium nitrate is higher than that of sodium hydrogen carbonate, we need to find the amount of sodium hydrogen carbonate that requires the same volume of water as the maximum solubility of potassium nitrate.
Let's start by converting the solubilities to the same units (grams per milliliter):
Potassium Nitrate:
31 grams / 100 ml = 0.31 grams / ml
Sodium Hydrogen Carbonate:
7.8 grams / 100 ml = 0.078 grams / ml
To achieve the smallest volume of water needed, we'll use the difference between the two solubilities:
0.31 grams / ml - 0.078 grams / ml = 0.232 grams / ml
Therefore, the smallest volume of water required to dissolve and remove potassium nitrate impurities while leaving pure sodium hydrogen carbonate is the volume that can hold 0.232 grams of potassium nitrate, which is approximately 1.02 ml.