A generic solid, X, has a molar mass of 60.2 g/mol. In a constant‑pressure calorimeter, 34.1 g of X is dissolved in 283 g of wat
er at 23.00 °C. X ( s ) ⟶ X ( aq ) The temperature of the resulting solution rises to 27.30 °C. Assume the solution has the same specific heat as water, 4.184 J/(g·°C), and that there is negligible heat loss to the surroundings. How much heat was absorbed by the solution?
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Answer:
Explanation:
When a spring is compressed, the force exerted by the spring is given by:
where
k is the spring constant
x is the compression of the spring
In this problem we have:
k = 52 N/m is the spring constant
x = 43 cm = 0.43 m is the compression
Therefore, the force exerted by the spring on the dart is
Now we can apply Newton' second law of motion to calculate the acceleration of the dart:
where
F = 22.4 N is the force exerted on the dart by the spring
m = 75 g = 0.075 kg is the mass of the dart
a is its acceleration
Solving for a,