Question

learn by doing
when 100 ml of 0.200 m nacl(aq) and 100 ml of 0.200 m agno₃(aq), both at 21.9°c, are mixed in a coffee cup calorimeter, the temperature increases to 23.5°c as solid agcl forms. calculate the value of q_reaction. assume the density and specific heat of the solutions are the same as water.
1300 j
670 j
-1300 j
-670 j
when solid ammonium nitrate dissolves in water, the solution becomes cold. this is the basis for an \instant ice pack\. when 6.71 g of solid nh₄no₃ dissolves in 50.0 g of water at 24.9°c in a calorimeter, the temperature decreases to 15.3°c. calculate the value of q for this reaction.
2280 j
-2280 j
2010 j
-2010 j

Explanation:

Step1: Calculate the mass of the solution for the first reaction

The total volume of the solution is \(V = 100\space mL+ 100\space mL=200\space mL\). Since the density of the solution is the same as water (\(
ho = 1\space g/mL\)), the mass of the solution \(m=
ho V=(1\space g/mL)\times200\space mL = 200\space g\).
The specific heat capacity of water \(c = 4.18\space J/(g\cdot^{\circ}C)\), and the temperature change \(\Delta T=T_{final}-T_{initial}=23.5^{\circ}C - 21.9^{\circ}C=1.6^{\circ}C\)
Using the formula \(q = mc\Delta T\), we have \(q_{solution}=(200\space g)\times(4.18\space J/(g\cdot^{\circ}C))\times(1.6^{\circ}C)=1337.6\space J\approx1300\space J\)
Since the reaction is exothermic (temperature increases), \(q_{reaction}=-q_{solution}=- 1300\space J\)

Step2: Calculate the mass of the solution for the second reaction

The mass of the solution \(m = 6.71\space g + 50.0\space g=56.71\space g\)
The specific heat capacity of water \(c = 4.18\space J/(g\cdot^{\circ}C)\), and the temperature change \(\Delta T=T_{final}-T_{initial}=15.3^{\circ}C - 24.9^{\circ}C=-9.6^{\circ}C\)
Using the formula \(q = mc\Delta T\), we have \(q_{solution}=(56.71\space g)\times(4.18\space J/(g\cdot^{\circ}C))\times(- 9.6^{\circ}C)\approx - 2280\space J\)
Since the reaction is endothermic (solution becomes cold), \(q_{reaction}=-q_{solution}=2280\space J\)

Answer:

For the first reaction: C. - 1300 J
For the second reaction: A. 2280 J