The molal boiling-point constant for water is 0.51 degrees C/molal. The boiling point of a 1.00 molal solution of Ca(NO3)2 should be increased by:
A.) exactly 1.53
or B.) Somewhat less than 1.53
This is how I worked the problem:
Ca(NO3)2 dislocates into 3 mole particles. Therefore, 3 x .51 x 1 molal = 1.53 elevation of boiling point. However, my teacher said the answer was B.) somewhat less than 1.53. What step would I be missing?
The van't Hoff factor of 3 which you have used is correct; however, in REAL terms, the three ions don't act as three but as somewhere between two and three. You may want to read about activity coefficients.
Based on your calculation, it seems correct that the boiling point of a 1.00 molal solution of Ca(NO3)2 should be increased by 1.53 degrees Celsius. However, it is important to consider the factors that may affect the accuracy of this value.
One possible factor is the assumption that Ca(NO3)2 completely dissociates into three moles of particles. In reality, not all compounds dissociate completely, so the actual number of particles may be less than three. This would result in a lower elevation of the boiling point compared to the calculated value of 1.53 degrees Celsius.
Additionally, the molal boiling-point constant for water, 0.51 degrees C/molal, is an approximate value. The actual value may vary slightly depending on experimental conditions.
Considering these factors, it is reasonable for the answer to be somewhat less than 1.53 degrees Celsius. However, without further information or clarification from your teacher, it is difficult to determine the exact value or reasoning behind choosing option B.
Based on your explanation, it seems like you have the correct approach for calculating the elevation of boiling point for a 1.00 molal solution of Ca(NO3)2. However, it is also important to consider any factors that may slightly affect the boiling point elevation, such as ionic interactions and dissociation constants.
In the case of calcium nitrate (Ca(NO3)2), it fully dissociates into three ions: one Ca2+ ion and two NO3- ions. These ions will interact with water molecules, affecting the boiling point elevation. This interaction can cause the observed boiling point elevation to be slightly less than the expected theoretical value.
The molal boiling-point constant is determined experimentally, taking into account such factors. Hence, the value of 0.51 degrees C/molal already accounts for any deviations that may occur.
Therefore, the answer should be A) exactly 1.53 degrees C, as you initially calculated. It's possible that there was a misunderstanding or miscommunication between you and your teacher. I would recommend discussing your approach and calculation with them to clarify any confusion.