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

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Homework Help Overview

The problem involves calculating the mass of NH₄Cl needed to lower the temperature of 1100 mL of water from 26°C to 15°C, illustrating an endothermic process. The heat of solution for NH₄Cl is provided, and the density of the solution is assumed to be the same as that of water.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculation of heat transfer using the formula Q = mcΔT and provide different mass estimates for NH₄Cl. There are questions regarding the assumptions made about the density of water and the mass of the solution.

Discussion Status

Multiple interpretations of the problem are being explored, with participants questioning the initial mass of water used in calculations and the implications of cooling the entire solution rather than just the water. Some guidance has been offered regarding the calculations, but no consensus has been reached on the correct approach.

Contextual Notes

There is a noted discrepancy in the density assumption of water at 26°C, and participants are considering the impact of including the mass of the NH₄Cl in the overall calculations.

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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.
 
Last edited:
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Show your work.
 
[tex]Q = mc\Delta T = (1100g)(4.18J g^-1 C^0^-1)(15C^0 - 26C^0) = -50kJ[/tex]

[tex]50kJ/14kJ/mol = 3.4mol[/tex]

[tex]3.4mol x (14g/mol + 4g/mol + 35.5g/mol) = 181.9g[/tex]
 
flyingpig said:
[tex]Q = mc\Delta T = (1100g)(4.18J g^-1 C^0^-1)(15C^0 - 26C^0) = -50kJ[/tex]
...
By rounding this intermediate result to -50kJ, you have reduced your answer by a little over 10%.
 
50578J/14700J = 3.44

3.44mol * 53.3g/mol = 184g

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