# 0.9 Quantitative aspects of chemical change  (Page 8/10)

 Page 8 / 10

## Using the combined gas law

1. An enclosed gas(i.e. one in a sealed container) has a volume of $300\phantom{\rule{2pt}{0ex}}\mathrm{cm}{}^{3}$ and a temperature of $300\phantom{\rule{2pt}{0ex}}\mathrm{K}$ . The pressure of the gas is $50\phantom{\rule{2pt}{0ex}}\mathrm{kPa}$ . Calculate the number of moles of gas that are present in the container.
2. What pressure will $3\phantom{\rule{2pt}{0ex}}\mathrm{mol}$ of gaseous nitrogen exert if it is pumped into a container that has a volume of $25\phantom{\rule{2pt}{0ex}}\mathrm{dm}{}^{3}$ at a temperature of $29\phantom{\rule{2pt}{0ex}}{}^{0}\phantom{\rule{2pt}{0ex}}\mathrm{C}$ ?
3. The volume of air inside a tyre is 19 litres and the temperature is $290\phantom{\rule{2pt}{0ex}}\mathrm{K}$ . You check the pressure of your tyres and find that the pressure is $190\phantom{\rule{2pt}{0ex}}\mathrm{kPa}$ . How many moles of air are present in the tyre?
4. Compressed carbon dioxide is contained within a gas cylinder at a pressure of 700 kPa. The temperature of the gas in the cylinder is $310\phantom{\rule{2pt}{0ex}}\mathrm{K}$ and the number of moles of gas is $13\phantom{\rule{2pt}{0ex}}\mathrm{mols}$ of carbon dioxide. What is the volume of the gas inside the cylinder?

## Molar concentrations of liquids

A typical solution is made by dissolving some solid substance in a liquid. The amount of substance that is dissolved in a given volume of liquid is known as the concentration of the liquid. Mathematically, concentration (C) is defined as moles of solute (n) per unit volume (V) of solution.

$C=\frac{n}{V}$

For this equation, the units for volume are $\mathrm{dm}{}^{3}$ . Therefore, the unit of concentration is $\mathrm{mol}·{\mathrm{dm}}^{-3}$ . When concentration is expressed in $\mathrm{mol}·{\mathrm{dm}}^{-3}$ it is known as the molarity (M) of the solution. Molarity is the most common expression for concentration.

Do not confuse molarity (M) with molar mass (M). Look carefully at the question in which the M appears to determine whether it is concentration or molar mass.
Concentration

Concentration is a measure of the amount of solute that is dissolved in a given volume of liquid. It is measured in $\mathrm{mol}·{\mathrm{dm}}^{-3}$ . Another term that is used for concentration is molarity (M)

If $3,5\phantom{\rule{2pt}{0ex}}\mathrm{g}$ of sodium hydroxide (NaOH) is dissolved in $2,5\phantom{\rule{2pt}{0ex}}{\mathrm{dm}}^{3}$ of water, what is the concentration of the solution in $\mathrm{mol}·{\mathrm{dm}}^{-3}$ ?

1. $n=\frac{m}{M}=\frac{3,5}{40}=0,0875\phantom{\rule{2pt}{0ex}}\mathrm{mol}$
2. $C=\frac{n}{V}=\frac{0,0875}{2,5}=0,035$

The concentration of the solution is $0,035\phantom{\rule{2pt}{0ex}}\mathrm{mol}·{\mathrm{dm}}^{-3}$ or $0,035\phantom{\rule{2pt}{0ex}}\mathrm{M}$

You have a $1\phantom{\rule{2pt}{0ex}}{\mathrm{dm}}^{3}$ container in which to prepare a solution of potassium permanganate ( $\mathrm{KMnO}{}_{4}$ ). What mass of $\mathrm{KMnO}{}_{4}$ is needed to make a solution with a concentration of $0,2\phantom{\rule{2pt}{0ex}}\mathrm{M}$ ?

1. $C=\frac{n}{V}$

therefore

$n=C×V=0,2×1=0,2\phantom{\rule{2pt}{0ex}}\mathrm{mol}$
2. $m=n×M=0,2×158,04=31,61\phantom{\rule{2pt}{0ex}}\mathrm{g}$

The mass of $\mathrm{KMnO}{}_{4}$ that is needed is $31,61\phantom{\rule{2pt}{0ex}}\mathrm{g}$ .

How much sodium chloride (in g) will one need to prepare $500\phantom{\rule{2pt}{0ex}}{\mathrm{cm}}^{3}$ of solution with a concentration of $0,01\phantom{\rule{2pt}{0ex}}\mathrm{M}$ ?

1. $V=\frac{500}{1 000}=0,5\phantom{\rule{2pt}{0ex}}{\mathrm{dm}}^{3}$
2. $n=C×V=0,01×0,5=0,005\phantom{\rule{2pt}{0ex}}\mathrm{mol}$
3. $m=n×M=0,005×58,45=0,29\phantom{\rule{2pt}{0ex}}\mathrm{g}$

The mass of sodium chloride needed is $0,29\phantom{\rule{2pt}{0ex}}\mathrm{g}$

## Molarity and the concentration of solutions

1. $5,95\phantom{\rule{2pt}{0ex}}\mathrm{g}$ of potassium bromide was dissolved in $400\phantom{\rule{2pt}{0ex}}{\mathrm{cm}}^{3}$ of water. Calculate its molarity.
2. $100\phantom{\rule{2pt}{0ex}}\mathrm{g}$ of sodium chloride (NaCl) is dissolved in $450\phantom{\rule{2pt}{0ex}}{\mathrm{cm}}^{3}$ of water.
1. How many moles of NaCl are present in solution?
2. What is the volume of water (in ${\mathrm{dm}}^{3}$ )?
3. Calculate the concentration of the solution.
4. What mass of sodium chloride would need to be added for the concentration to become $5,7\phantom{\rule{2pt}{0ex}}\mathrm{mol}·{\mathrm{dm}}^{-3}$ ?
3. What is the molarity of the solution formed by dissolving $80\phantom{\rule{2pt}{0ex}}\mathrm{g}$ of sodium hydroxide ( $\mathrm{NaOH}$ ) in $500\phantom{\rule{2pt}{0ex}}{\mathrm{cm}}^{3}$ of water?
4. What mass (g) of hydrogen chloride ( $\mathrm{HCl}$ ) is needed to make up $1000\phantom{\rule{2pt}{0ex}}{\mathrm{cm}}^{3}$ of a solution of concentration $1\phantom{\rule{2pt}{0ex}}\mathrm{mol}·{\mathrm{dm}}^{-3}$ ?
5. How many moles of $\mathrm{H}{}_{2}\mathrm{SO}{}_{4}$ are there in $250\phantom{\rule{2pt}{0ex}}{\mathrm{cm}}^{3}$ of a $0,8\phantom{\rule{2pt}{0ex}}\mathrm{M}$ sulphuric acid solution? What mass of acid is in this solution?

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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Damian Reply
absolutely yes
Daniel
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Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
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Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
What makes metals better to use as wires than non-metals? (please link to bonding type)??? HELP
Yash Reply

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Source:  OpenStax, Chemistry grade 10 [caps]. OpenStax CNX. Jun 13, 2011 Download for free at http://cnx.org/content/col11303/1.4
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