A famous chemical company in Oman hired you as a research chemist. On the very first day of your job, your senior asked you to determine the density of a newly discovered unknown metal. In your lab, two liquids named X and Y are
available with densities of 3.0771 g/mL and 4.0017 g/mL respectively. In the process of finding density you made a
mixture of these liquids and drop a small object of that unknown metal, however, you notice that the object becomes
suspended in the liquid; that is, it neither sinks nor floats. If the mixture was made of 32.77 percent X and 67.23 percent
Y by volume, what is the density of the metal?
Select one:
a. 7.398 g/mL.
b. 2.413 g/mL
c. 2.360 g/mL
d. 3.699 g/mL
e. 3.539 g/mL

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Explanation:

when 25.0 ml of 0.700 mol/l naoh was mixed in a calorimeter with 25.0 ml of 0.700 mol/l hcl, both initially at 20.0 °c, the temperature increased to 22.1 °c. the heat capacity of the calorimeter is 279 j/°c.

the equation for the reaction is:

naoh + hcl → nacl + h₂o

moles of hcl = 0.0250 l hcl ×

0.700

mol hcl

1 l hcl = 0.0175 mol hcl

volume of solution = (25.0 + 25.0) ml = 50.0 ml

mass of solution = 50.0 ml soln ×

1.00

ml soln

= 50.0 g soln

δt=t2-t1

= (22.1 – 20.0) °c = 2.1 °c

the heats involved are

heat from neutralization + heat to warm solution + heat to warm calorimeter = 0

q1+q2+q3=0

nδh+mcδt+cδt=0

0.0175 mol ×

δh

+ 50.0 g × 4.184 j·g⁻¹°c⁻¹ × 2.1 °c + 279 j°c⁻¹ × 2.1 °c = 0

0.0175 mol ×

δh

+ 439.32 j + 585.9 j = 0

0.0175 mol ×

δh

= -1025.22 j

δh=1025.22j0.0175 mol= -58 600 j/mol = -58.6 kj/mol