Characteristics and Measurable properties of gases Questions in English

(B) Liquids and gases possess the ability to flow because their molecules are not held in fixed positions and can move past one another freely. Due to this characteristic property of flowing,they are collectively referred to as fluids.

(N/A) Dalton$'$s law of partial pressures states that for a mixture of non-reacting gases,the total pressure exerted by the mixture is equal to the sum of the partial pressures of the individual gases.
Mathematically,it is expressed as: $P_{total} = p_1 + p_2 + p_3 + \dots + p_n$ (at constant temperature and volume),
where $P_{total}$ is the total pressure of the mixture and $p_1, p_2, \dots, p_n$ are the partial pressures of the individual gases.

(A) The boiling point of sulfur dioxide $(SO_2)$ is $263 \ K$.

(C) The state of matter is primarily determined by the balance between the intermolecular forces and the thermal energy of the particles.
Factors such as $Temperature$,$Pressure$,$Volume$,and $Mass$ (or amount of substance) are the key variables that influence the physical state of matter,i.e.,$Solid$,$Liquid$,or $Gas$.

(B) When a gas is collected over water,it becomes saturated with water vapours,which exert their own partial pressure known as aqueous tension.
The total pressure observed $(P_{\text{moist gas}})$ is the sum of the partial pressure of the dry gas and the aqueous tension:
$P_{\text{moist gas}} = P_{\text{dry gas}} + P_{\text{aqueous tension}}$
To obtain the pressure of the dry gas,we rearrange the equation:
$P_{\text{dry gas}} = P_{\text{moist gas}} - P_{\text{aqueous tension}}$
Therefore,the correction term applied is to subtract the aqueous tension from the total pressure.

(N/A) Two phenomena that can be explained on the basis of surface tension are as follows:
$(i)$ Rise or fall of a liquid in a capillary tube (capillary action).
$(ii)$ Spherical shape of small liquid drops.

(N/A) As the temperature of a liquid is increased,the kinetic energy of the molecules increases,which helps to overcome the intermolecular forces. Consequently,the liquid flows more easily,which results in a decrease in the viscosity of the liquid.

(N/A) When a liquid flows over a fixed surface,the layer of molecules in contact with the surface is stationary.
As the distance of the layers from the fixed surface increases,the velocity of the upper layers increases.
This type of flow,in which there is a regular gradation of velocity when passing from one layer to the next,is called laminar flow.
In laminar flow,the velocity of molecules is not the same in all the layers because every layer offers some resistance or friction to the layer immediately below it,resulting in a velocity gradient.

(A) The three main states of matter are:
$(i)$ Solid
$(ii)$ Liquid
$(iii)$ Gas
Additionally,there are other states like Plasma and $BEC$ (Bose-Einstein Condensate).

(A) The kinetic energy of particles depends on the state of matter.
In solids,particles are tightly packed with minimal movement,resulting in the lowest energy.
In liquids,particles have more freedom of movement than in solids.
In gases,particles move randomly at high speeds,resulting in the highest energy.
Therefore,the increasing order of energy is $Solid < Liquid < Gas$.

(A) Thermal energy is directly related to the motion of particles.
In solids,particles are fixed in position and have the least thermal energy.
In liquids,particles have more freedom of movement than in solids.
In gases,particles move randomly at high speeds,possessing the highest thermal energy.
Therefore,the increasing order of thermal energy is: $Solid < Liquid < Gas$.

(B) The strength of intermolecular forces is directly related to the proximity of particles.
In gases,particles are far apart,so intermolecular forces are weakest.
In liquids,particles are closer than in gases,so forces are stronger.
In solids,particles are tightly packed,resulting in the strongest intermolecular forces.
Therefore,the order of increasing intermolecular forces is: $Gas < Liquid < Solid$.

(D) The measurable properties of a gas are:
$(i)$ Mass
$(ii)$ Volume
$(iii)$ Temperature
$(iv)$ Pressure
Therefore,all these properties are measurable for a gas.

(N/A)

Property	$SI$ Unit
$(i)$ Mass	Kilogram $(kg)$
$(ii)$ Volume	Cubic meter $(m^3)$
$(iii)$ Temperature	Kelvin $(K)$
$(iv)$ Pressure	Pascal $(Pa)$ or $(N \cdot m^{-2})$

Note: $1 \, m^3 = 10^3 \, dm^3 = 1000 \, L = 10^6 \, cm^3$ and $1 \, atm = 101325 \, Pa$.

(A) The different units of gas pressure are as follows:
$(i)$ $SI$ unit: Pascal $(Pa)$
$(ii)$ Bar $(bar)$
$(iii)$ Atmosphere $(atm)$
$(iv)$ Torr $(torr)$

$(i) \ 1 \, atm = 101.325 \, kPa = 101325 \, Pa = 101325 \, N \, m^{-2}$
$(ii) \ 1 \, bar = 10^5 \, Pa = 10^2 \, kPa = 10^5 \, N \, m^{-2}$
$(iii) \ 1 \, atm = 1.01325 \, bar$
$(iv) \ 1 \, atm = 76 \, cm \, Hg = 760 \, mm \, Hg = 760 \, torr$
$(v) \ 1 \, torr = 1 \, mm \, Hg$
Note: $1 \, bar$ is approximately equal to $1 \, atm$,but they are not identical.

(A) The kinetic energy of particles depends on the state of matter.
In solids,particles are tightly packed and have the least kinetic energy.
In liquids,particles have more freedom of movement than in solids.
In gases,particles move randomly at high speeds,possessing the highest kinetic energy.
Therefore,the order of kinetic energy is: $Solid < Liquid < Gas$.

(B) The correct answer is $Liquid$.
Liquids have a definite volume because the intermolecular forces are strong enough to keep the molecules together,but they do not have a definite shape because the molecules can slide past each other,allowing the liquid to take the shape of the container.

(A) $1 \, bar = 10^{5} \, Pa$.
This value represents the atmospheric pressure at sea level.

(A) Since these cities are located at sea level,the atmospheric pressure at $0\,^oC$ $(273.15\,K)$ is considered the standard atmospheric pressure.
Therefore,the pressure is $1\,bar$ or $10^{5}\,Pa$.

(N/A) $STP$ (Standard Temperature and Pressure) is defined as $273.15 \ K$ and $1 \ bar$ pressure. The molar volume of an ideal gas at $STP$ is $22.71 \ L \ mol^{-1}$.
$SATP$ (Standard Ambient Temperature and Pressure) is defined as $298.15 \ K$ and $1 \ bar$ pressure. The molar volume of an ideal gas at $SATP$ is $24.79 \ L \ mol^{-1}$.

(A) The absolute temperature scale,also known as the Kelvin scale,is defined such that $0 \ K$ is equivalent to $-273.15^{\circ}C$.
This scale is related to the Celsius scale by the equation: $T(K) = t(^{\circ}C) + 273.15$.

(N/A) According to Dalton's law of partial pressure,the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
The mathematical expression is:
$p_{total} = p_1 + p_2 + p_3 + \ldots + p_n$ $(i)$
Since $p_i = \frac{n_i RT}{V}$,the expression can be written as:
$p_{total} = (n_1 + n_2 + \ldots + n_n) \frac{RT}{V}$ (ii)

(A) When a gas is collected over water,it becomes moist and contains water vapor. The total pressure observed is the sum of the partial pressure of the dry gas and the vapor pressure of water (aqueous tension).
According to Dalton's Law of Partial Pressures: $P_{\text{total}} = P_{\text{dry gas}} + P_{\text{water vapor}}$.
Therefore,the pressure of the dry gas is calculated as: $P_{\text{dry gas}} = P_{\text{total}} - P_{\text{water vapor}}$.

(N/A) $(i) \text{ Partial pressure } = p_{1} = \frac{n_{1} RT}{V} \dots (i)$
$(ii) \text{ Partial pressure } = p_{1} = x_{1} p_{\text{total}} \dots (ii)$
$(iii) \text{ Partial pressure } = p_{1} = \text{Volume percentage of gas} \times \frac{p_{\text{total}}}{100}$

(A) According to Dalton's Law of Partial Pressures,the total pressure $(P_{total})$ of a mixture of non-reacting gases is equal to the sum of their partial pressures.
$P_{total} = P_{CO_2} + P_{CH_4}$
Given:
$P_{total} = 8.3 \times 10^4 \, Pa$
$P_{CO_2} = 2.8 \times 10^4 \, Pa$
Substituting the values:
$8.3 \times 10^4 \, Pa = 2.8 \times 10^4 \, Pa + P_{CH_4}$
$P_{CH_4} = (8.3 - 2.8) \times 10^4 \, Pa$
$P_{CH_4} = 5.5 \times 10^4 \, Pa$

(C) The payload is defined as the difference between the mass of the air displaced by the balloon and the total mass of the balloon.

(B) Gases are highly compressible because there are large intermolecular spaces between the gas molecules. When pressure is applied,these molecules come closer to each other,significantly reducing the volume.

(A) At $STP$,since there are negligible forces of attraction between gas molecules,gases expand to occupy the entire available space of the container. Therefore,a gas occupies the volume of the container.

(N/A) $(i)$ Gases are highly compressible.
$(ii)$ Gases mix easily and diffuse throughout the available space.
$(iii)$ Gases do not have a definite shape or volume.
$(iv)$ There is negligible intermolecular attraction between gas molecules.

(B) According to Graham's Law of Diffusion,the rate of diffusion $(r)$ is inversely proportional to the square root of the molar mass $(M)$: $r \propto \frac{1}{\sqrt{M}}$.
For $NH_3$,$M = 17 \ g/mol$.
For $H_2S$,$M = 34 \ g/mol$.
Since $NH_3$ has a lower molar mass than $H_2S$,it diffuses faster and will be detected first.

(A) Dry air has a higher density than moist air.
This is because dry air consists of $N_2$ $(28 \ g/mol)$,$O_2$ $(32 \ g/mol)$,and $CO_2$ $(44 \ g/mol)$,which have higher molar masses.
In moist air,some of these molecules are replaced by water vapor $(H_2O)$,which has a lower molar mass of $18 \ g/mol$.
According to Avogadro's law,at constant temperature and pressure,the density of a gas is directly proportional to its molar mass. Therefore,replacing heavier air molecules with lighter water vapor molecules decreases the overall density of the air.

(B, C) Dalton's Law of Partial Pressure applies only to non-reacting gas mixtures.
$(i)$ $CO_2 + O_2 + N_2$ and $(iv)$ $HCl + O_2$ are non-reacting mixtures,so the law applies.
$(ii)$ $CO + O_2$ and $(iii)$ $NH_3 + HCl$ are reacting mixtures,so the law does not apply.
Chemical reactions:
$(ii)$ $2CO + O_2 \rightarrow 2CO_2$
$(iii)$ $NH_3 + HCl \rightarrow NH_4Cl$

(A) For most liquids,viscosity increases with an increase in pressure because the molecules are forced closer together,increasing intermolecular forces.
Exception: For water $(H_2O)$,the viscosity decreases with an increase in pressure at temperatures below $32 \ ^\circ C$.

(B) The molecules in a liquid are not held in fixed positions and can move freely past one another. This property allows the liquid to flow,be poured,and take the shape of the container it is placed in.

(D) The important physical properties of liquids are:
$(i)$ Vapour pressure
$(ii)$ Surface tension
$(iii)$ Viscosity

(N/A) When a liquid is partially filled in an evacuated closed container at a constant temperature,an equilibrium is established between the liquid phase and the vapor phase after some time. The vapor pressure at this equilibrium state is called 'equilibrium vapor pressure' or 'saturated vapor pressure'.

(C) The vapor pressure of a liquid depends on two main factors:
$(i)$ Temperature: As the temperature increases,the kinetic energy of the molecules increases,leading to higher vapor pressure.
$(ii)$ Nature of the liquid: Liquids with weaker intermolecular forces have higher vapor pressure at a given temperature.

(N/A) The temperature at which the vapor pressure of a liquid becomes equal to the external atmospheric pressure is called the boiling point of that liquid.
Normal boiling point: The boiling point at $1 \ atm$ pressure is called the normal boiling point.
Standard boiling point: The boiling point at $1 \ bar$ pressure is called the standard boiling point of the liquid.

(N/A) The boiling point is lower on a mountain. This is because the atmospheric pressure is lower at higher altitudes compared to the seashore.

(A) Surgical instruments are sterilized in an autoclave because it operates at a pressure higher than atmospheric pressure.
This increased pressure raises the boiling point of water,allowing steam to reach temperatures above $100 \ ^\circ C$.
This high-temperature steam effectively kills bacteria and microorganisms,ensuring complete sterilization.

(B) Definition: Surface tension is defined as the force acting per unit length perpendicular to the line drawn on the surface of the liquid.
Mathematical expression: $\gamma = \frac{F}{l}$
Dimensions: The force $F$ has dimensions $[MLT^{-2}]$ and length $l$ has dimensions $[L]$. Thus,surface tension has dimensions $[MLT^{-2}] / [L] = [MT^{-2}]$.
$SI$ unit: Since force is measured in $N$ and length in $m$,the $SI$ unit is $N m^{-1}$ (or $kg \ s^{-2}$).

(B) liquid has its lowest energy state when its surface area is minimized. For a given volume,a sphere has the minimum surface area. Therefore,in the absence of external forces,liquid droplets tend to be $Spherical$ to minimize their surface energy.

(C) The magnitude of surface tension depends on the strength of the attractive forces between the molecules.
Stronger intermolecular forces result in higher surface tension.
Surface tension decreases with an increase in temperature because increased kinetic energy reduces the effective intermolecular attraction.

(B) Viscosity is a measure of the internal resistance to flow offered by one layer of liquid to another layer while moving past each other.

(C) The force $F$ required to maintain the flow of layers in a liquid depends on:
$(i)$ The area of contact of the layers $(A)$.
$(ii)$ The velocity gradient $\left(\frac{dv}{dz}\right)$.
According to Newton's law of viscosity,$F \propto A$ and $F \propto \frac{dv}{dz}$.
Therefore,$F = \eta A \left(\frac{dv}{dz}\right)$,where $\eta$ is the coefficient of viscosity.

(N/A) The force $F$ required to maintain the flow of layers in a liquid is given by the formula:
$F = \eta A \frac{dv}{dz}$
where $\eta = \frac{F}{A(dv/dz)}$.
Here,$\eta$ is the constant of proportionality and is called the coefficient of viscosity.
If the contact area $A = 1$ unit and the velocity gradient $\frac{dv}{dz} = 1$,then $\eta = F$.
Thus,the coefficient of viscosity $(\eta)$ is the force required when the velocity gradient and the contact area are unity.
Its $SI$ unit is $N \cdot s \cdot m^{-2}$ or $Pa \cdot s$ (Pascal-second).
In $kg \cdot m^{-1} \cdot s^{-1}$,the unit is $1 \ kg \cdot m^{-1} \cdot s^{-1} = 1 \ Pa \cdot s$.
The $CGS$ unit is $Poise$ $(P)$.
$1 \ P = 1 \ g \cdot cm^{-1} \cdot s^{-1} = 0.1 \ kg \cdot m^{-1} \cdot s^{-1}$.

(N/A) $(1)$ Intermolecular forces
$(2)$ Van der Waals forces
$(3)$ Dispersion forces
$(4)$ $V = k_2T$

(N/A) $(1)$ Absolute zero
$(2)$ Partial pressure
$(3)$ Aqueous tension
$(4)$ Temperature

(N/A) $(1)$ Robert Boyle
$(2)$ $\frac{1}{r^3}$
$(3)$ $\frac{1}{r^6}$
$(4)$ $10$ to $100$