1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
prisoha [69]
3 years ago
7

Making the simplistic assumption that the dissolved NaCl(s) does not affect the volume of the solvent water, determine the const

ants m and b in the equation Molarity = mdensity + b that relates the NaCl molarity to the NaCl(aq) density. Take the density of water to be 1.00 g/mL and the molar mass of NaCl to be 58.5 g/mol.
I am having a very difficult time answering this question. There just doesn't seem to be enough information to determine the constants.
Chemistry
2 answers:
shtirl [24]3 years ago
7 0

Answer:

  • m = 1,000/58.5
  • b = - 1,000 / 58.5

1) Variables

  • molarity: M
  • density of the solution: d
  • moles of NaCl: n₁
  • mass of NaCl: m₁
  • molar mass of NaCl: MM₁
  • total volume in liters: Vt
  • Volume of water in mililiters: V₂
  • mass of water: m₂

2) Density of the solution: mass in grams / volume in mililiters

  • d = [m₁ + m₂] / (1000Vt)

3) Mass of NaCl: m₁

    Number of moles = mass in grams / molar mass

    ⇒ mass in grams = number of moles × molar mass

        m₁ = n₁ × MM₁


4) Number of moles of NaCl: n₁

   Molarity = number of moles / Volume of solution in liters

   M = n₁ / Vt

   ⇒ n₁ = M × Vt


5) Substitue in the equation of m₁:

   m₁ = M × Vt × MM₁


6) Substitute in the equation of density:

    d = [M × Vt × MM₁ + m₂] / (1000Vt)


7) Simplify and solve for M

  • d = M × Vt × MM₁ / (1000Vt) + m₂/ (1000Vt)
  • d = M × MM₁ / (1000) + m₂/ (1000Vt)

Making the simplistic assumption that the dissolved NaCl(s) does not affect the volume of the solvent water means 1000Vt = V₂  

  • d = M × MM₁ / (1000) + m₂/ V₂

        m₂/ V₂ is the density of water: 1.00 g/mL

  • d = M × MM₁ / (1000) + 1.00 g/mL
  • M × MM₁ / (1000) = d - 1.00 g/mL
  • M = [1,000/MM₁] d - 1,000/ MM₁

8) Substituting MM₁ = 58.5 g/mol

  • M = [1,000/58.5] d - [1,000/ 58.5]

Comparing with the equation Molarity = m×density + b, you obtain:

  • m = 1,000/58.5
  • b = - 1,000/58.5
sashaice [31]3 years ago
6 0

The value of m is \boxed{{\text{1/molar mass}}\left({0.0170\;{\text{mol}}\cdot{{\text{g}}^{-1}}}\right)} and the value of b is \boxed{{\text{mol/volume}}}.

Further Explanation:

The property is a unique feature of the substance that differentiates it from the other substances. It is classified into two types:

1. Intensive properties:

These are the properties that depend on the nature of the substance. These don't depend on the size of the system. Their values remain unaltered even if the system is further divided into a number of subsystems. Temperature, refractive index, molarity, concentration, pressure, and density are some of the examples of intensive properties.

2. Extensive properties:

These are the properties that depend on the amount of the substance. These are additive in nature when a single system is divided into many subsystems. Mass, enthalpy, volume, energy, size, weight, and length are some of the examples of extensive properties.

Density is defined as the ratio between mass and volume. Both mass and volume are the physical properties that are extensive in nature and their ratio comes out to be an intensive quantity that depends only on the nature of the substance, not on the amount of the substance. The formula to calculate the density of a substance is,

{\text{Density of substance}}\left({{\rho }}\right){\text{=}}\frac{{{\text{Mass of substance}}\left({\text{M}}\right)}}{{{\text{Volume of substance}}\left({\text{V}}\right)}}

Molarity is a concentration term that is defined as the number of moles of solute dissolved in one litre of the solution. It is denoted by M and its unit is mol/L.

The formula to calculate the molarity of the solution is as follows:

{\text{Molarity of solution}}=\frac{{{\text{amount}}\;\left({{\text{mol}}}\right)\;{\text{of}}\;{\text{solute}}}}{{\;{\text{volume}}\left({\text{L}}\right)\;{\text{of}}\;{\text{solution}}}}

The given expression is,

{\text{Molarity}}={\text{m}}\left({{\text{density}}}\right)+{\text{b}}           …… (1)

Substitute the formula of given quantities in equation (1).

\frac{{{\text{mol}}}}{{{\text{Volume}}}}={\text{m}}\left({\frac{{{\text{mass}}}}{{{\text{Volume}}}}}\right)+{\text{b}}                          …… (2)

Quantities with same units are added, subtracted, multiplied or divided. So two quantities on the right-hand side of equation (2) must have the same units and equation (2) becomes,

\frac{{{\text{mol}}}}{{{\text{Volume}}}}={\text{m}}\left({\frac{{{\text{mass}}}}{{{\text{Volume}}}}}\right)+{\text{m}}\left({\frac{{{\text{mass}}}}{{{\text{Volume}}}}}\right)                                 …… (3)

Solve for units of m,

{\text{m}}=\frac{{{\text{mol}}}}{{{\text{mass}}}}

Or it can be written as,

{\text{m}}=\frac{{\text{1}}}{{{\text{Molar mass}}}}                               …… (4)

Substitute 58.5 g/mol for the molar mass of NaCl in equation (4).

\begin{aligned}{\text{m}}&=\frac{{{\text{1 mol}}}}{{{\text{58}}{\text{.5 g}}}}\\&=0.0170\;{\text{mol}}\cdot{{\text{g}}^{-1}}\\\end{aligned}

The unit of b is equal to that of m(density). So its unit can be calculated as follows:

\begin{aligned}{\text{b}}&=\left({\frac{{{\text{mol}}}}{{{\text{mass}}}}}\right)\left({\frac{{{\text{mass}}}}{{{\text{Volume}}}}}\right)\\&=\frac{{{\text{mol}}}}{{{\text{Volume}}}}\\\end{aligned}

Learn more:

1. Rate of chemical reaction: brainly.com/question/1569924

2. The main purpose of conducting experiments: brainly.com/question/5096428

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Keys to studying chemistry

Keywords: Property, intensive, extensive, physical properties, chemical properties, density, substance, amount, quantity, nature, molarity, units, m, b, mol/L, mol/volume, molar mass.

You might be interested in
Write down moleculer formula:
Temka [501]
1. Ca(HCO3)2
2.Ca(HCOO)2
3. Ca(OH)2
4.NaOH
5.KCI
6.MgSO4
7.PbO
8.HCl
9.HNO3
10.H2SO4
11.NH3
12.(NH4)3PO4
13.NaOH
:)
5 0
3 years ago
Read 2 more answers
How lead and iodine compound formed
ale4655 [162]
These are dissolved in water to form colourless solutions, and then mixed together. This mixing leads to a double displacement reaction, essentially resulting in the metals 'swapping' their places in the two compounds, producing lead (II) iodide, and potassium nitrate.
3 0
2 years ago
Which carboxylic acid has the lowest boiling point?
erik [133]
Methanoic acid :33333
7 0
2 years ago
Tengo que resolver con procedimiento
zzz [600]

Answer:

Distance = 200 km

Distance = 204 km

Speed = 77 km/h

Time = 21.42 h

Explanation:

Given:

A.

Speed = 100 km/h , Time = 2 h

Find:

Distance

B.

Speed = 68 km/h , Time = 3 h

Find:

Distance

C.

Distance = 154 km , Time = 2 h

Find:

Speed

D.

Distance = 1500 km speed = 70 km/h

Find:

Time

Computation:

Speed = distance / time

A.

Distance = 100 x 2

Distance = 200 km

B.

Distance = 68 x 3

Distance = 204 km

C.

Speed = 154 / 2

Speed = 77 km/h

D.

Time = 1500 / 70

Time = 21.42 h

6 0
2 years ago
Find the number of mol-atom in 7.1 gr cl
marin [14]
I don’t know if this would help but my cousin said this: Molecular weight of chlorine = 71, so 7.1/71 = 0.1 mol of Cl2
7 0
2 years ago
Other questions:
  • How many molecules of o2 are required to form 13.5 g of water vapor?
    7·1 answer
  • A sample of gas contains 0.1500 mol of HCl(g) and 7.500×10-2 mol of Br2(g) and occupies a volume of 9.63 L. The following reacti
    11·1 answer
  • Which state of matter has a definite volume, but does not have a definite shape?
    11·1 answer
  • What is the molecular formula of a compound with an empirical formula of C4H9 and a gram-formula mass of 114.0 g/mole?
    8·1 answer
  • What is the oxidation number for CO2
    13·1 answer
  • Please help me!!!!!!!!!!
    8·1 answer
  • Steel is an alloy of one or more elements combined with which metal?
    14·1 answer
  • How can I differentiate between Ionic compounds, molecular compounds, and acids given only the formula? I need to be able to fin
    13·1 answer
  • Suppose that 33.3 J of heat is added to an ideal gas. The gas expands at a constant pressure of 1.45 104 Pa while changing its v
    14·1 answer
  • Sigh.....................................
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!