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zhenek
1 month ago
9

Leonard adds 5 grams of sugar to 1 liter of water to make one sugar solution. Then he adds 10 grams of sugar to 1 liter of water

to make another sugar solution. Which statement correctly compares these solutions?
Chemistry
1 answer:
castortr0y [3K]1 month ago
7 0

Answer:

Please refer to the explanation below.

Explanation:

There are numerous claims and methods to compare both solutions, the most common being concentration (or molarity) and %m/V.

Though both comparisons are valid, molarity is preferable since it provides a single figure indicating which solution is more concentrated.

To calculate the molarity of any solution, we use this formula:

M = n/V

n: the number of moles of solute.

V: the volume of the solution in liters.

As the solvent is water and the solute is a solid, the volume of the solution equals the solvent’s volume.

The common type of sugar, sucrose, has the molecular formula C12H22O11, with a molar mass of 342.3 g/mol.

This allows us to calculate the moles:

n = m/MM

n₁ = 5/342.3 = 0.0146 moles

n₂ = 10/342.3 = 0.0292 moles

Now, let’s determine the concentration of each solution:

M₁ = 0.0146 / 1 = 0.0146 M

M₂ = 0.0292 / 1 = 0.0293 M

Thus, we conclude that the second solution is more concentrated than the first. In other terms, M₂ > M₁

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66.667 mL of 3.000 M H2SO4 (aq) solution was neutralized by the stoichiometric amount of 4.000 M Al(OH)3 solution in a coffee cu
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Answer:

\large \boxed{\Delta_{\textbf{r}}H =\text{-4600 J$\cdot$ mol}^{-1}}

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This scenario is unrealistic since Al(OH)₃ is not soluble in water.

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B. Calorimetry — where we assess the enthalpy of the reaction.

A. Stoichiometry

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                 2Al(OH)₃ + 3H₂SO₄ ⟶ Al₂(SO₄)₃ + 6H₂O

M/V:            66.667

c/mol·L⁻¹:   4.000       3.000

(b) Moles of H₂SO₄

\rm \text{66.667 mL H$_{2}$}SO_{4} \times \dfrac{\text{3.000 mmol H$_{2}$SO}_{4}}{\text{1 mL H$_{2}$SO}_{4}} = \text{200.00 mmol H$_{2}$SO}_{4}

(c) Moles of Al(OH)₃

The molar ratio stands at 2 mmol Al(OH)₃: 3 mmol H₂SO₄

\text{Moles of Al(OH)}_{3} = \text{200.00 mmol of H$_{2}$SO}_{4} \times \dfrac{\text{2 mmol Al(OH)}_{3}}{\text{3 mmol H$_{2}$SO}_{4}}\\\\= \text{133.33 mmol Al(OH)}_{3}

(d) Volume of Al(OH)₃

\text{Moles of Al(OH)}_{3} = \text{200.00 mmol of H$_{2}$SO}_{4} \times \dfrac{\text{1 mL Al(OH)}_{3}}{\text{4 mmol H$_{2}$SO}_{4}} = \text{50.000 mL Al(OH)}_{3}

B. Calorimetry

This reaction has two energy exchanges.

q₁ = heat from the reaction

q₂ = heat used to heat the calorimeter

 q₁ + q₂ = 0

nΔH + mCΔT = 0

Data:

Moles of Al₂(SO₄)₃ = 0.066 667 mol

C = 1.10 J°C⁻¹g⁻¹

T_initial = 22.3 °C

T_final = 24.7 °C

Calculations

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Assume solutions are as dense as water (though not realistic).

Mass of sulfuric acid solution            =   66.667 g 

Mass of aluminium hydroxide solution =  50.000    

                                             TOTAL =  116.667 g

(b) ΔT

ΔT = T_final - T_initial = 24.7 °C - 22.3 °C = 2.4°C

(c) ΔH

\begin{array}{ccccl}n\Delta H & +& mC \Delta T& = &0\\\text{0.066 667 mol }\times \Delta H& + & \text{116.667 g} \times 1.10 \text{ J$^{\circ}$C$^{-1}$g$^{-1}$} \times 2.4 \, ^{\circ}\text{C} & = & 0\\0.066667 \Delta H \text{ mol} & + & \text{310 J} & = & 0\\&&0.066667 \Delta H \text{ mol} & = & \text{-310 J} & & \\\end{array}\\

\begin{array}{ccccl}& &\Delta H & = & \dfrac{\text{-310 J}}{\text{0.066667 mol}}\\\\& &\Delta H & = & \textbf{-4600 kJ/mol}\\\end{array}\\\large \boxed{\mathbf{\Delta_{\textbf{r}}H} =\textbf{-4600 J$\cdot$ mol}^{\mathbf{-1}}}

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