My answer key is wrong right? I can't get it right

[flyingpig]

Homework Statement

You are planning a lecture demonstration to illustrate an endothermic process. You want to lower the temperature of 1100 mL water in an insulated container from 26C to 15C

Approximately what mass of NH₄Cl should you dissolve in the water to achieve this result? The heat of solution of NH₄Cl is +14.7kJ/mol NH₄Cl. Assume that the density of dilute is the same as that of water.

The Attempt at a Solution

I tried 1.8 x 10² g, but it is wrong.

 

[D H]

Show your work.

 

[flyingpig]

$$Q = mc\Delta T = (1100g)(4.18J g^-1 C^0^-1)(15C^0 - 26C^0) = -50kJ$$

$$50kJ/14kJ/mol = 3.4mol$$

$$3.4mol x (14g/mol + 4g/mol + 35.5g/mol) = 181.9g$$

 

[SammyS]

$$Q = mc\Delta T = (1100g)(4.18J g^-1 C^0^-1)(15C^0 - 26C^0) = -50kJ$$
...

By rounding this intermediate result to -50kJ, you have reduced your answer by a little over 10%.

 

[flyingpig]

50578J/14700J = 3.44

3.44mol * 53.3g/mol = 184g

Which is still wrong

 

[D H]

Where did that 1100 grams come from? Being perhaps a bit too pedantic, the density of water at 26°C is not 1 gram/cc.

Much more importantly, you are cooling the water-ammonium chloride solution, not just the water. This alone makes that 1100 gram figure incorrect and is the primary source of your error.

 

[flyingpig]

Lol our professor showed us how to do it today because even he got it wrong when he did it.