To find out how much water is required to make a saturated solution of barium nitrate at 100°C, we can use the given solubility information.
The solubility of barium nitrate at 100°C is 34 g/100 g of water. This means that 100 g of water can dissolve 34 g of barium nitrate.
If we start with 100 g of barium nitrate, we need to determine the amount of water required to dissolve it completely. We can set up a proportion using the solubility information:
(34 g of Ba(NO3)2) / (100 g of H2O) = (100 g of Ba(NO3)2) / (x g of H2O)
Cross-multiplying, we get:
34g * x = 100 g * 100 g
x = (100 g * 100 g) / 34 g
x ≈ 294 g of H2O
Therefore, to make a saturated solution of barium nitrate at 100°C, approximately 294 g of water is required.
Now, let's determine how much barium nitrate precipitates out of solution when the saturated solution is cooled to 0°C.
The solubility of barium nitrate at 0°C is 5.0 g/100 g of water. This means that 100 g of water can dissolve 5.0 g of barium nitrate.
The amount of water in the saturated solution at 0°C will still be 294 g, as water does not evaporate during the cooling process.
To find out how much barium nitrate precipitates, we can subtract the amount of barium nitrate that remains dissolved at 0°C from the initial amount added.
The initial amount of barium nitrate added was 100 g.
We can set up a proportion using the solubility information at 0°C:
(5.0 g of Ba(NO3)2) / (100 g of H2O) = (x g of Ba(NO3)2) / (294 g of H2O)
Cross-multiplying, we get:
5.0 g * 294 g = 100 g * x
1470 g = 100 g * x
x = 1470 g / 100 g
x ≈ 14.7 g of Ba(NO3)2
Therefore, when the saturated solution is cooled to 0°C, approximately 14.7 g of barium nitrate will precipitate out of solution.
Additionally, since the precipitated crystals carry along with them 4 g of water per 100 g of crystals, we can calculate the amount of water carried by the precipitated barium nitrate.
The amount of barium nitrate precipitated is approximately 14.7 g.
(4 g H2O / 100 g Ba(NO3)2) x (14.7 g Ba(NO3)2) ≈ 0.588 g of H2O.
Therefore, approximately 0.588 g of water will be carried along with the precipitated barium nitrate crystals.