A gas that follows Boyle’s law,
Question: A gas that follows Boyles law, Charles law and Avogadros law is called an ideal gas. Under what conditions a real gas would behave ideally? Solution: At high temperature and low pressure, the gases behave ideally since the two postulates of kinetic theory of gases are true under these conditions. (i) The volume of a molecule of a gas is negligible as compared to its complete volume. (ii) There is negligible force of attraction between the molecules of a gas....
Read More →What will be the molar volume
Question: What will be the molar volume of nitrogen and argon at 273.15K and 1 atm? Solution: We know that 1 mole of any gases at STP (273K, 1 atm) occupies a volume of 22.4L. The molar volume (volume of 1 mole of the gas), therefore these gases occupy 22.4L of volume....
Read More →What will be the molar volume
Question: What will be the molar volume of nitrogen and argon at 273.15 K and 1 atm? Solution: When temperature and pressure of a gas are 273.15 K (or 0C) and 1 atm (or 1 bar or 105pascal), such conditions are called standard temperature and pressure conditions (STP). Under these conditions, the volume occupied by 1 mole of each and every gas is 22.4 L. Hence, the molar volume of N2and Ar at 273.15 K and 1 atm is 22,4 L....
Read More →Use the information and data given below
Question: Use the information and data given below to answer the questions (a) to (c): Stronger intermolecular forces result in a higher boiling point. Strength of London forces increases with the number of electrons in the molecule. Boiling point of HF, HCl, HBr and HI is 293 K, 189 K, 206 K and 238 K respectively. (a) Which type of intermolecular forces are present in the molecules HF, HCl, HBr and HI? (b) Looking at the trend of boiling points of HCl, HBr and HI, explain out of dipole-dipole ...
Read More →The behaviour of matter in different states
Question: The behaviour of matter in different states is governed by various physical laws. According to you what are the factors that determine the state of matter? Solution: The factors that determine the states of matter can be determined by 2 laws. Charles Law It states that when pressure is kept constant, the volume of an ideal gas (V) is directly proportional to the absolute temperature (T). V1/T1 = V2/T2 Boyles Law. It states that when the temperature is kept constant, the pressure of the...
Read More →Find the angle to intersection of the following curves:
Question: Find the angle to intersection of the following curves: $x^{2}+y^{2}=2 x$ and $y^{2}=x$ Solution: Given: Curves $x^{2}+y^{2}=2 x \ldots(1)$ $\ y^{2}=x \ldots(2)$ Solving $(1) \(2)$, we get Substituting $y^{2}=x$ in $x^{2}+y^{2}=2 x$ $\Rightarrow x^{2}+x=2 x$ $\Rightarrow x^{2}-x=0$ $\Rightarrow x(x-1)=0$ $\Rightarrow x=0$ or $(x-1)=0$ $\Rightarrow x=0$ or $x=1$ Substituting $x=0$ or $x=1$ in $y^{2}=x$, we get, when $x=0$ $\Rightarrow y^{2}=0$ $\Rightarrow y=0$ when $x=1$ $\Rightarrow y...
Read More →Physical properties of ice,
Question: Physical properties of ice, water and steam are very different. What is the chemical composition of water in all the three states? Solution: The chemical composition of water remains the same in all the physical states, i.e., solid, liquid and gas....
Read More →Show that the points A
Question: Show that the points $\mathbf{A}(1,1), \mathbf{B}(-1,-1)$ and $\mathbf{C}(-\sqrt{3}, \sqrt{3})$ are the vertices of an equilateral triangle each of whose sides is 22 units. Solution: Given: The 3 points are $A(1,1), B(-1,-1)$ and $C(-\sqrt{3}, \sqrt{3})$. $A B=\sqrt{(-1-1)^{2}+(-1-1)^{2}}$ $=\sqrt{4+4}$ $=2 \sqrt{2}$ units ..(1) $B C=\sqrt{(-\sqrt{3}+1)^{2}+(\sqrt{3}+1)^{2}}$ $=\sqrt{3-2 \sqrt{3}+1+3+2 \sqrt{3}+1}$ $=2 \sqrt{2}$ units ..(2) $A C=\sqrt{(-\sqrt{3}-1)^{2}+(\sqrt{3}-1)^{2}...
Read More →Show that the points A
Question: Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle. Solution: Given: The 3 points are $A(7,10), B(-2,5)$ and $C(3,-4)$ $A B=\sqrt{(-2-7)^{2}+(5-10)^{2}}$ $=\sqrt{81+25}$ $=\sqrt{106}$ units ..(1) $B C=\sqrt{(3+2)^{2}+(-4-5)^{2}}$ $=\sqrt{25+81}$ $=\sqrt{106}$ units ..(2) $A C=\sqrt{(3-7)^{2}+(-4-10)^{2}}$ $=\sqrt{16+196}$ $=\sqrt{2} 12$ units From equations 1 and 2, we have ⇒ AB = BC Therefore, Δ ABC is an isosceles triangle ..(3...
Read More →Find the angle to intersection of the following curves :
Question: Find the angle to intersection of the following curves : $x^{2}=27 y$ and $y^{2}=8 x$ Solution: Given: Curves $x^{2}=27 y \ldots(1)$ $\ y^{2}=8 x \ldots(2)$ Solving $(1) \(2)$, we get, From $y^{2}=8 x$, we get, $\Rightarrow x=\frac{y^{2}}{8}$ Substituting $x=\frac{y^{2}}{8}$ on $x^{2}=27 y$, $\Rightarrow\left(\frac{y^{2}}{8}\right)^{2}=27 y$ $\Rightarrow\left(\frac{y^{4}}{64}\right)=27 y$ $\Rightarrow y^{4}=1728 y$ $\Rightarrow y\left(y^{3}-1728\right)=0$ $\Rightarrow y=0$ or $\left(y^...
Read More →Using the distance formula, show that the points A
Question: Using the distance formula, show that the points A(3, -2), B(5, 2) and C(8,8) are collinear. Solution: Given: The 3 points are A(3, -2), B(5, 2) and C(8, 8). $A B=\sqrt{(5-3)^{2}+(2+2)^{2}}$ $=\sqrt{4+16}$ $=2 \sqrt{5}$ units $B C=\sqrt{(8-5)^{2}+(8-2)^{2}}$ $=\sqrt{9+36}$ $=3 \sqrt{5}$ units $A C=\sqrt{(8-3)^{2}+(8+2)^{2}}$ $=\sqrt{25+100}$ $=5 \sqrt{5}$ units ..(3) From equations 1, 2 and 3, we have ⇒ AC = AB + BC This is possible only if the points are collinear. Therefore, the poin...
Read More →Find the angle to intersection of the following curves:
Question: Find the angle to intersection of the following curves: $x^{2}+4 y^{2}=8$ and $x^{2}-2 y^{2}=2$ Solution: Given: Curves $x^{2}+4 y^{2}=8 \ldots(1)$ $\ x^{2}-2 y^{2}=2 \ldots(2)$] Solving $(1) \(2)$, we get, from 2 nd curve, $x^{2}=2+2 y^{2}$ Substituting on $x^{2}+4 y^{2}=8$, $\Rightarrow 2+2 y^{2}+4 y^{2}=8$ $\Rightarrow 6 y^{2}=6$ $\Rightarrow y^{2}=1$ $\Rightarrow y=\pm 1$ Substituting on $y=\pm 1$, we get, $\Rightarrow x^{2}=2+2(\pm 1)^{2}$ $\Rightarrow x^{2}=4$ $\Rightarrow x=\pm ...
Read More →If 1 gram of each of the following gases
Question: If 1 gram of each of the following gases are taken at STP, which of the gases will occupy (a) greatest volume and (b) smallest volume? CO, H20, CH4, NO Solution: Molar volume of a gas is volume occupied by 1 mole of gas at STP $(273.15$ $\mathrm{K}$ and 1 bar pressure) and is equal to $22700 \mathrm{~mL}$ $28 \mathrm{~g}$ of $\mathrm{CO}$ occupy volume $=22700 \mathrm{~mL}$ $\therefore 1 \mathrm{~g}$ of CO occupies volume $=\frac{22700}{28} \mathrm{~mL}$ at STP Similarly, $1 \mathrm{~g...
Read More →Find a point on the y-axis which is equidistant from A
Question: Find a point on the $y$-axis which is equidistant from $A(-4,3)$ and $B(5,2)$. Solution: Let the point on the y-axis be P(0, y) Given: $P$ is equidistant from $A(-4,3)$ and $B(5,2)$. i.e., PA = PB $\Rightarrow \sqrt{(-4-0)^{2}+(3-y)^{2}}=\sqrt{(5-0)^{2}+(2-y)^{2}}$ Squaring both sides, we get $\Rightarrow(-4-0)^{2}+(3-y)^{2}=(5-0)^{2}+(2-y)^{2}$ $\Rightarrow 16+9-6 y+y^{2}=25+4-4 y+y^{2}$ $\Rightarrow 25-6 y=29-4 y$ $\Rightarrow 2 y=-4$ $\Rightarrow y=-2$ Therefore, the required point ...
Read More →Which of the following changes decrease
Question: Which of the following changes decrease the vapour pressure of water kept in a sealed vessel? (a) Decreasing the quantity of water (b) Adding salt to water (c) Decreasing the volume of the vessel to one-half (d) Decreasing the temperature of water Solution: (b, d) Vapour pressure does not depend upon the quantity of water or size of the vessel. It decreases on adding salt to water or decreasing the temperature of water....
Read More →Under which of the following two conditions
Question: Under which of the following two conditions applied together, a gas deviates most from the ideal behaviour? (a) Low pressure (b) High pressure (c) Low temperature (d) High temperature Solution: (b, c) A gas which obeys the ideal gas equation, p V = nRTunder all conditions of temperature and pressure is called an ideal gas. However, there is no gas which obeys the ideal gas equation under all conditions of temperature and pressure. Hence, the concept of ideal gas is only theoretical or ...
Read More →Which of the following figures does
Question: Which of the following figures does not represent 1 mole of dioxygen gas at STP? (a) 16 grams of gas (b) 22.7 litres of gas (c) 6.022 x 1023dioxygen molecules (d) 11.2 litres of gas Solution: (a, d) 1 mole of dioxygen represents 32 g of 02, 22.7 L of 02or 6.022 x 1023molecules of o2gas....
Read More →A is a point on the x-axis with abscissa -8 and B is a point on the
Question: $A$ is a point on the $x$-axis with abscissa $-8$ and $B$ is a point on the $y$-axis with ordinate 15. Find the distance AB. Solution: Given: The two points are $A(-8,0)$ and $B(0,15)$ Distance between A and B $=\sqrt{(0+8)^{2}+(15-0)^{2}}$ $\Rightarrow \sqrt{64+225}$ $\Rightarrow \sqrt{289}$ $\Rightarrow 17$ units Therefore, the distance between A and B is 17 units....
Read More →With regard to the gaseous state of matter
Question: With regard to the gaseous state of matter which of the following statements are correct? (a) Complete order of molecules (b) Complete disorder of molecules (c) Random motion of molecules (d) Fixed position of molecules Solution: (b, c) In gaseous state, molecules are in a state of random motion, i.e., it is the state in which molecules are disorderly arranged. Gaseous state has higher entropy than the liquid as well as solid....
Read More →Find the angle to intersection of the following curves:
Question: Find the angle to intersection of the following curves: $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ and $x^{2}+y^{2}=a b$ Solution: Given: Curves $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ .......(1) $\ x^{2}+y^{2}=a b \ldots(2)$ Second curve is $x^{2}+y^{2}=a b$ $y^{2}=a b-x^{2}$ Substituting this in equation (1), $\Rightarrow \frac{x^{2}}{a^{2}}+\frac{a b-x^{2}}{b^{2}}=1$ $\Rightarrow \frac{x^{2} b^{2}+a^{2}\left(a b-x^{2}\right)}{a^{2} b^{2}}=1$ $\Rightarrow x^{2} b^{2}+a^{3} b-a^{...
Read More →How does the surface tension of
Question: How does the surface tension of a liquid vary with increase in temperature? (a) Remains same (b) Decrease (c) Increase (d) No regular pattern is followed Solution: (b) Surface tension of a liquid decreases with increase in temperature due to less forces of attraction between the molecules....
Read More →Increase in kinetic energy can overcome
Question: Increase in kinetic energy can overcome intermolecular forces of attraction. How will the viscosity of liquid be affected by the increase in temperature? (a)Increase (b)No effect (c) Decrease (d) No regular pattern will be followed Solution: (c) Intermolecular force of liquid decreases with increase in temperature, hence viscosity of liquid also decreases. However, some exceptions are there like liquid proteins and liquid sulphur....
Read More →Atmospheric pressures recorded in different
Question: Atmospheric pressures recorded in different cities are as follows: Cities Shimla Bangalore Delhi Mumbai p in N/m2 1.01105 1.2105 1.02105 1.21105 Consider the above data and mark the place at which liquid will boil first. (i) Shimla (ii) Bangalore (iii) Delhi (iv) Mumbai Solution: Option (i) is the answer....
Read More →Find the distance between the points A
Question: Find the distance between the points $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$, when (i) $\mathrm{AB}$ is parallel to the $\mathrm{x}$-axis (ii) $A B$ is parallel to the $y$-axis. Solution: (i) Given: AB is parallel to the x-axis. When AB is parallel to the x-axis, the y co-ordinate of A and B will be the same. i.e., $y_{1}=y_{2}$ Distance $=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{1}-y_{1}\right)^{2}}$ $\Rightarrow\left|x_{2}-x_{1}\right|$ Therefore the distance...
Read More →What is the SI unit of viscosity
Question: What is the SI unit of viscosity coefficient ()? (i) Pascal (ii) Nsm2 (iii) km2 s (iv) N m2 Solution: Option (ii) is the answer....
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