8. when a 2.5 mol of sugar (c12h22o11) are added to a certain amount of water the boiling point is raised by 1 celsius degree. if 2.5 mol of aluminum nitrate is added to the same amount of water, by how much will the boiling point be changed? show all calculations leading to your answer or use 3 – 4 sentences to explain your answer.

The boiling point of the water by adding 2.5 moles of aluminium nitrate will be changed by 4° C.

Explanation:

Step 1: define the formula for an elevation of the boiling point

Δ T b  = i *K b *bB

⇒with Δ T b = the elevation of the boiling point ( in °C or Kelvin)

⇒with i = van't Hoff  i -factor for the solute. The factor i shows the number of individual particles (typically ions) that are formed by a compound in the solution.

⇒ with Kb = ebullioscopic constant, which depends on the properties of the solvent. (Eventually can be calculated).

⇒ with bB= the molal concentration (molality) of the solute.

Since we have 2 different solutions ( component 1 = sugar and component 2 = aluminium nitrate) of the same molality in the same solvent ( water). We can express this as followed:

Δ T b,2 / Δ T b,1  = (i2 * Kb * bB ) / (i1 * Kb *bB)

⇒after he was simplifying this becomes:

Δ T b,2 / Δ T b,1  = i2 / i1

⇒ Now we can isolate either Δ T b,2 or Δ T b,1:

Δ T b,2  =(i2/i1) x Δ T b,1

Sugar

⇒ is a covalent compound, so it doesn't dissociate in water ⇔ i1=1

Aluminium nitrate

⇒ it's a soluble ionic compound and in solution it will dissociate as the following equation:

Al(NO3)3 (aq) → Al3+(aq)  + 3NO3- (aq)

⇒thus here are 4 particels formed : 1 Al3+ + 3NO3-

i2=4

As given, we also know that the temperature was raised by 1°C after adding sugar ⇒ Δ T b,1 = 1°C

Step 2: insert all the numbers in the formula for boiling point elevation

(i2/i1) x Δ T b,1

(4/1 ) x 1°C = 4°C

⇒ The boiling point of the water by adding 2.5 moles of aluminium nitrate will be changed by 4°C

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