A 0.60 L portion of a 1.2 M AgNO3 solution is mixed with a 0.3 L potion of a 1.2 M Na2CrO4 solution in an constant pressure calorimeter. Upon mixing, the solid Ag2CrO4 is formed and the heart released is 48.2 kJ. The specific heat of the solution is 4.18 J/C*g and the final density is 1.009 g/ml. What is the temperature change of the solution?
48,200 = mass x specific heat x delta T.
mass = 900 mL x 1.009 g/mL
Solve for delta T.
To determine the temperature change of the solution, we can use the equation q = mcΔT, where q is the heat released or absorbed, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the change in temperature.
First, let's calculate the mass of the solution. We can find the mass using the density of the solution:
Density = mass/volume
Given that the final density is 1.009 g/ml, we can multiply this by the total volume of the solution (0.60 L + 0.30 L) to find the mass:
Mass = Density × Volume
Mass = 1.009 g/ml × (0.60 L + 0.30 L) = 1.009 g/ml × 0.90 L
Next, we need to convert the units of mass from grams/ml to grams. Since 1 ml = 1 cm^3, we can use the following conversion:
1 g/ml = 1 g/cm^3
So the mass of the solution is:
Mass = 1.009 g/cm^3 × 0.90 L = 0.9081 kg
Now, let's calculate the heat released or absorbed (q). We are given that the heat released is 48.2 kJ. Remember that 1 kJ = 1000 J, so we need to convert kJ to J:
q = 48.2 kJ × 1000 J/1 kJ = 48200 J
Now we have all the information needed to find the temperature change (ΔT). Rearranging the equation q = mcΔT, we can solve for ΔT:
ΔT = q / (m × c)
Substituting the values into the equation:
ΔT = 48200 J / (0.9081 kg × 4.18 J/C*g) = T1
Evaluating this expression, we find T1:
T1 ≈ 136.58 °C
So, the temperature change of the solution is approximately 136.58 °C.