If you lived in Flagstaff, Arizona, how much salt (NaCl) would you have to add to your spaghetti water to get it to boil at 100 oC. Assume you are using 2 quarts of water in your spaghetti pot. Report the amount of salt in units you might actually be able to measure in your kitchen. If you have a scale that shows grams that will be okay. (Hint: To get started find out the actual boiling point of water in Flagstaff.) It is at an elevation above 7000 ft.)

Explanation:

This question is both theoretical and practical. While the theoretical aspect will be detailed fully here, the practical aspect will be provided as a form of guidance.

Water generally boils at 100°C when altitude (in feet) is 0. One of the colligative properties that occurs when salt is added to water is that there is a boiling point elevation(meaning an increase in boiling point). For instance, if 20g of salt is added to about 5.3 quarts of water, the boiling point of water will increase from 100°C to 100.04°C.

However, when the altitude/elevation of a place is about 7000 ft (like in Flagstaff, Arizona), water will boil at 95.3°C. In order to get 2 quarts of water to boil at 100°C in Flagstaff;

20g causes an increase in boiling point by 0.04°C (100°C to 100.04°C) in 5.3 quarts of water

What gram will increase the boiling point by same 0.04°C in 2 quarts

20g ⇒ 5.3

X ⇒ 2

5.3 X ⇒ 40g

X = 40 ÷ 5.3

X = 7.55g

Hence, 7.55g will cause an increase in boiling point by 0.04°C (from 100°C to 100.04°C) in 2 quarts of water

What mass of salt will increase the boiling point by 4.7°C (95.3°C to 100°C)

7.55g ⇒ 0.04

X ⇒ 4.7

X × 0.04 ⇒ 7.55 × 4.7

0.04X ⇒ 35.5

X = 887.5g

Hence, in order for the spaghetti water to boil at 100°C, 887.5g of salt needs to be added.

For the practical part of the question, some Kitchen scales have an accuracy of .25kg (250g) and some have an accuracy of .2 kg (200g) and some have an accuracy of .5kg (500g). The one your kitchen has will determine the amount of salt that you can measure. For example, if your kitchen scale/balance has an accuracy of 250g/0.25kg, then you can only measure 750g of the 887.5g (as the rest is 137.5g, which is not up to 250g of the scale's accuracy) of the required salt measurement. However, if you have a digital balance that can measure up to 2kg/2000g in one decimal place, that's the perfect balance to measure this salt.

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