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4 years ago

If you mix 95 degrees C and 5 degrees C what temperature would you get?

Chemistry

1 answer:

forsale [732]4 years ago

4 0

Answer:

Between $5^oC$ and $95^oC$

Explanation:

According to the second law of thermodynamics, heat flows from hotter objects toward colder objects.

Having a mixture of two components, one at a higher temperature of $95^oC$ and the other one at a lower temperature of $5^oC$ , heat will flow from the first object to the second one.

The temperature of the first object will decrease and the temperature of the second object will increase. Assuming no phase change, the final equilibrium temperature will be reached between $5^oC$ and $95^oC$ .

We cannot tell the exact temperature, unless we know the specific heat capacity of each material and their masses. The first object will give off heat given by:

$Q_1 = c_1m_1(95^oC - t_f)$

The second object will gain this heat by:

$Q_2 = c_2m_2(t_f - 5^oC)$

Since the heat given off is equal to the heat gained:

$c_1m_1(95^oC - t_f) = c_2m_2(t_f - 5^oC)$

Let's say that each object is water with a specific heat capacity of:

$c_1 = c_2 = 4.184 \frac{J}{g^oC}$

The mass of the first object is 10 g, the mass of the second one is 50 g, then:

$4.184 \frac{J}{g^oC}\cdot 10 g\cdot (95^oC - t_f) = 4.184 \frac{J}{g^oC}\cdot 50 g\cdot (t_f - 5^oC)$

The equation is simplified to:

$950 - 10t_f = 50t_f - 250$

$60t_f = 1200$

$t_f = 20^oC$

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2 years ago

A solution contains 0.0440 M Ca2 and 0.0940 M Ag. If solid Na3PO4 is added to this mixture, which of the phosphate species would

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Answer:

C. $Ca_3(PO_4)_2$ will precipitate out first

the percentage of $Ca^{2+}$ remaining = 12.86%

Explanation:

Given that:

A solution contains:

$[Ca^{2+}] = 0.0440 \ M$

$[Ag^+] = 0.0940 \ M$

From the list of options , Let find the dissociation of $Ag_3PO_4$

$Ag_3PO_4 \to Ag^{3+} + PO_4^{3-}$

where;

Solubility product constant Ksp of $Ag_3PO_4$ is $8.89 \times 10^{-17}$

Thus;

$Ksp = [Ag^+]^3[PO_4^{3-}]$

replacing the known values in order to determine the unknown ; we have :

$8.89 \times 10 ^{-17} = (0.0940)^3[PO_4^{3-}]$

$\dfrac{8.89 \times 10 ^{-17}}{(0.0940)^3} = [PO_4^{3-}]$

$[PO_4^{3-}] =\dfrac{8.89 \times 10 ^{-17}}{(0.0940)^3}$

$[PO_4^{3-}] =1.07 \times 10^{-13}$

The dissociation of $Ca_3(PO_4)_2$

The solubility product constant of $Ca_3(PO_4)_2$ is $2.07 \times 10^{-32}$

The dissociation of $Ca_3(PO_4)_2$ is :

$Ca_3(PO_4)_2 \to 3Ca^{2+} + 2 PO_{4}^{3-}$

Thus;

$Ksp = [Ca^{2+}]^3 [PO_4^{3-}]^2$

$2.07 \times 10^{-33} = (0.0440)^3 [PO_4^{3-}]^2$

$\dfrac{2.07 \times 10^{-33} }{(0.0440)^3}= [PO_4^{3-}]^2$

$[PO_4^{3-}]^2 = \dfrac{2.07 \times 10^{-33} }{(0.0440)^3}$

$[PO_4^{3-}]^2 = 2.43 \times 10^{-29}$

$[PO_4^{3-}] = \sqrt{2.43 \times 10^{-29}$

$[PO_4^{3-}] =4.93 \times 10^{-15}$

Thus; the phosphate anion needed for precipitation is smaller i.e $4.93 \times 10^{-15}$ in $Ca_3(PO_4)_2$ than in $Ag_3PO_4$ $1.07 \times 10^{-13}$

Therefore:

$Ca_3(PO_4)_2$ will precipitate out first

To determine the concentration of $[Ca^+]$ when the second cation starts to precipitate ; we have :

$Ksp = [Ca^{2+}]^3 [PO_4^{3-}]^2$

$2.07 \times 10^{-33} = [Ca^{2+}]^3 (1.07 \times 10^{-13})^2$

$[Ca^{2+}]^3 = \dfrac{2.07 \times 10^{-33} }{(1.07 \times 10^{-13})^2}$

$[Ca^{2+}]^3 =1.808 \times 10^{-7}$

$[Ca^{2+}] =\sqrt[3]{1.808 \times 10^{-7}}$

$[Ca^{2+}] =0.00566$

This implies that when the second cation starts to precipitate ; the concentration of $[Ca^{2+}]$ in the solution is 0.00566

Therefore;

the percentage of $Ca^{2+}$ remaining = concentration remaining/initial concentration × 100%

the percentage of $Ca^{2+}$ remaining = 0.00566/0.0440 × 100%

the percentage of $Ca^{2+}$ remaining = 0.1286 × 100%

the percentage of $Ca^{2+}$ remaining = 12.86%

5 0

4 years ago