Solve the following
Question: $6.023 \times 10^{22}$ molecules are present in $10 \mathrm{~g}$ of a substance ' $x$ '. The molarity of a solution containing $5 \mathrm{~g}$ of substance ' $x$ ' in $2 \mathrm{~L}$ solution is______________ $\times 10^{-3}$. Solution: (25) Number of mole of $x=\frac{6.022 \times 10^{22}}{6.022 \times 10^{23}}=\frac{10}{\text { Molar mass of } x}$ So molar mass of $x=100 \mathrm{~g}$ Molarity $=\frac{5}{100 \times 2}=0.025 \mathrm{M}$....
Read More →The mole fraction of glucose
Question: The mole fraction of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ in an aqueous binary solution is $0.1$. The mass percentage of water in it, to the nearest integer, is ___________ . Solution: (47) Let total mole of solution $=1$ So, mole of glucose $=0.1$ Mole of $\mathrm{H}_{2} \mathrm{O}=0.9$ $=47.368=47.37$...
Read More →Write the next term of the AP
Question: Write the next term of the AP $\sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots \ldots$ Solution: The given $\mathrm{AP}$ is $\sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots$ On simplifying the terms, we get: $2 \sqrt{2}, 3 \sqrt{2}, 4 \sqrt{2}, \ldots$ Here, $a=2 \sqrt{2}$ and $d=(3 \sqrt{2}-2 \sqrt{2})=\sqrt{2}$ $\therefore$ Next term, $\mathrm{T}_{4}=a+3 d=2 \sqrt{2}+3 \sqrt{2}=5 \sqrt{2}=\sqrt{50}$...
Read More →The nth term of an AP is (7 − 4n). Find its common difference.
Question: Thenth term of an AP is (7 4n). Find its common difference. Solution: We have:Tn= (7 - 4n)Common difference =T2-T1T1= 7 - 4⨯ 1= 3T2=7 - 4⨯ 2 = -1d= -1 - 3 = -4Hence, the common difference is -4....
Read More →The ratio of the mass percentages of '
Question: The ratio of the mass percentages of ' $\mathrm{C} \ \mathrm{H}$ ' and ' $\mathrm{C} \ \mathrm{O}$ ' of a saturated acyclic organic compound ' $\mathrm{X}$ ' are $4: 1$ and $3: 4$ respectively. Then, the moles of oxygen gas required for complete combustion of two moles of organic compound ' $X$ ' is ____________ . Solution: (5)...
Read More →The nth term of an AP is (3n + 5). Find its common difference.
Question: Thenth term of an AP is (3n+ 5). Find its common difference. Solution: We have:Tn= (3n+ 5)Common difference = T2- T1T1= 3⨯ 1 + 5 = 8T2=3⨯ 2+ 5 = 11d= 11 - 8 = 3Hence, the common difference is 3....
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsIfandenotes thenth term of the AP 2, 7, 12, 17, ... , find the value of (a30a20). Solution: The given AP is 2, 7, 12, 17, ... .Here,a= 2 andd= 7 2 = 5 $\therefore a_{30}-a_{20}$ $=[2+(30-1) \times 5]-[2+(20-1) \times 5] \quad\left[a_{n}=a+(n-1) d\right]$ $=147-97$ $=50$ Hence, the required value is 50....
Read More →Solve the following
Question: The $\mathrm{NaNO}_{3}$ weighed out to make $50 \mathrm{~mL}$ of an aqueous solution containing $70.0 \mathrm{mgNa}^{+}$per $\mathrm{mL}$ is ___________ g.(Rounded off to the nearest integer) [Given: Atomic weight in $\mathrm{g}$ mol $^{-1}$. Na: $23 ; \mathrm{N}: 14 ; \mathrm{O}: 16$ ] Solution: (13) $\mathrm{Na}^{+}=70 \mathrm{mg} / \mathrm{mL}$ $\mathrm{W}_{\text {Nat }}$ in $50 \mathrm{~mL}$ solution $=70 \times 50 \mathrm{mg}$ $=3500 \mathrm{mg}$ $=3.5 \mathrm{gm}$ Moles of $\math...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsWhat is the 5th term from the end of the AP 2, 7, 12, ..., 47? Solution: The given AP is 2, 7, 12, ..., 47.Let us re-write the given AP in reverse order i.e. 47, 42, ..., 12, 7, 2.Now, the 5th term from the end of the given AP is equal to the 5th term from beginning of the AP 47, 42, ..., 12, 7, 2.Consider the AP 47, 42, ..., 12, 7, 2.Here,a= 47 andd= 42 47 = 55th term of this AP= 47 + (5 1) (5)= 47 20= 27Hence, the 5th term from the end of the give...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsWhat is the sum of firstnterms of the APa, 3a, 5a, ... . Solution: The given AP isa, 3a, 5a, ... .Here,First term,A=aCommon difference,D= 3aa= 2a Sum of firstnterms,Sn $=\frac{n}{2}[2 \times a+(n-1) \times 2 a] \quad\left\{S_{n}=\frac{n}{2}[2 A+(n-1) D]\right\}$ $=\frac{n}{2}(2 a+2 a n-2 a)$ $=\frac{n}{2} \times 2 a n$ $=a n^{2}$ Hence, the required sum isan2....
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsIf the sum of firstmterms of an AP is (2m2+ 3m) then what is its second term? Solution: LetSmdenotes the sum of firstmterms of the AP. $\therefore S_{m}=2 m^{2}+3 m$ $\Rightarrow S_{m-1}=2(m-1)^{2}+3(m-1)=2\left(m^{2}-2 m+1\right)+3(m-1)=2 m^{2}-m-1$ Now, $m^{\text {th }}$ term of the AP, $a_{m}=S_{m}-S_{m-1}$ $\therefore a_{m}=\left(2 m^{2}+3 m\right)-\left(2 m^{2}-m-1\right)=4 m+1$ Puttingm= 2, we get $a_{2}=4 \times 2+1=9$ Hence, the second term ...
Read More →The number of significant figures in
Question: The number of significant figures in $50000.020 \times 10^{-3}$ is Solution: (7) $50000.020 \times 10^{-3}$ Number of significant figure $=7$...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsHow many three-digit natural numbers are divisible by 9? Solution: The three-digit natural numbers divisible by 9 are 108, 117, 126, ..., 999.Clearly, these number are in AP.Here,a= 108 andd= 117 108 = 9 $a_{n}=999$ $\Rightarrow 108+(n-1) \times 9=999 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 9 n+99=999$ $\Rightarrow 9 n=999-99=900$ $\Rightarrow n=100$ Hence, there are 100 three-digit numbers divisible by 9.Let this AP containsnterms. Then,...
Read More →Solve the following
Question: In basic medium $\mathrm{CrO}_{4}^{2-}$ oxidizes $\mathrm{S}_{2} \mathrm{O}_{3}^{2-}$ to form $\mathrm{SO}_{4}^{2-}$ and itself changes into $\mathrm{Cr}(\mathrm{OH})_{4}^{-}$. The volume of $0.154 \mathrm{MCrO}_{4}^{2-}$ required to react with $40 \mathrm{~mL}$ of $0.25 \mathrm{MS}_{2} \mathrm{O}_{3}{ }^{2-}$ is _______________. (Rounded-off to the nearest integer) Solution: (173) $17 \mathrm{H}_{2} \mathrm{O}+8 \mathrm{CrO}_{4}+3 \mathrm{~S}_{2} \mathrm{O}_{3} \longrightarrow 6 \math...
Read More →Complete combustion of 1.80 g
Question: Complete combustion of $1.80 \mathrm{~g}$ of an oxygen containing compound $\left(\mathrm{C}_{\mathrm{x}} \mathrm{H}_{\mathrm{y}} \mathrm{O}_{\mathrm{z}}\right)$ gave $2.64 \mathrm{~g}$ of $\mathrm{CO}_{2}$ and $1.08 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$. The percentage of oxygen in the organic compound is:$63.53$$53.33$$51.63$$50.33$Correct Option: , 2 Solution:...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsHow many three-digit natural numbers are divisible by 7? Solution: The three-digit natural numbers divisible by 7 are 105, 112, 119, ..., 994.Clearly, these number are in AP.Here,a= 105 andd= 112 105 = 7Let this AP containsnterms. Then, $a_{n}=994$ $\Rightarrow 105+(n-1) \times 7=994 \quad\left[a_{n}=a+(n-1) d\right]$ $\Rightarrow 7 n+98=994$ $\Rightarrow 7 n=994-98=896$ $\Rightarrow n=128$ Hence, there are 128 three-digit numbers divisible by 7....
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsIf the numbers (2n 1), (3n+ 2) and (6n 1) are in AP, find the value ofnand the numbers. Solution: It is given that the numbers (2n 1), (3n+ 2) and (6n 1) are in AP. $\therefore(3 n+2)-(2 n-1)=(6 n-1)-(3 n+2)$ $\Rightarrow 3 n+2-2 n+1=6 n-1-3 n-2$ $\Rightarrow n+3=3 n-3$ $\Rightarrow 2 n=6$ $\Rightarrow n=3$ Whenn= 3, $2 n-1=2 \times 3-1=6-1=5$ $3 n+2=3 \times 3+2=9+2=11$ $6 n-1=6 \times 3-1=18-1=17$ Hence, the required value ofnis 3 and the numbers ...
Read More →1.86 g of aniline completely reacts to form acetanilide.
Question: $1.86 \mathrm{~g}$ of aniline completely reacts to form acetanilide. $10 \%$ of the product is lost during purificatiion. Amount of acetanilide obtained after purification (in g) is _____________$\times 10^{-2}$ Solution: (243) Molar mass $=93$ Molar mass $=135$ $93 \mathrm{~g}$ Aniline produce $135 \mathrm{~g}$ acetanilide $1.86 \mathrm{~g}$ produce $\frac{135 \times 1.86}{93}=2.70 \mathrm{~g}$ At $10 \%$ loss, $90 \%$ product will be formed after purification. Amount of product obtai...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsIf the numbersa, 9,b, 25 form an AP, findaandb. Solution: It is given that the numbersa, 9,b, 25 form an AP. $\therefore 9-a=b-9=25-b$ So, $b-9=25-b$ $\Rightarrow 2 b=34$ $\Rightarrow b=17$ Also, $9-a=b-9$ $\Rightarrow a=18-b$ $\Rightarrow a=18-17 \quad(b=17)$ $\Rightarrow a=1$ Hence, the required values ofaandbare 1 and 17, respectively....
Read More →4.5g of compound A (MW=90) was used to make 250 mL of its aqueous solution.
Question: $4.5 \mathrm{~g}$ of compound $A(\mathrm{MW}=90)$ was used to make $250 \mathrm{~mL}$ of its aqueous solution. The molarity of the solution in $\mathrm{M}$ is $\mathrm{x} \times 10^{-1}$. The value of $\mathrm{x}$ is_____________ . (Rounded off to the nearest integer) Solution: (2)...
Read More →Consider the above reaction where
Question: Consider the above reaction where $6.1 \mathrm{~g}$ of benzoic acid is used to get $7.8 \mathrm{~g}$ of $\mathrm{m}$-bromo benzoic acid. The percentage yield of the product is _______________ . (Round off to the Nearest integer) [Given : Atomic masses : $\mathrm{C}=12.0 \mathrm{u}, \mathrm{H}: 1.0 \mathrm{u}$,$\mathrm{O}: 16.0 \mathrm{u}, \mathrm{Br}=80.0 \mathrm{u}]$ Solution: (78) Moles of Benzoic acid $=\frac{6.1}{122}=$ moles of $\mathrm{m}$-bromobenzoic acid So, weight thel mobenz...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsIf 18,a, (b 3) are in AP, then find the value of (2ab). Solution: It given that 18,a, (b 3) are in AP. $\therefore a-18=(b-3)-a$ $\Rightarrow a+a-b=18-3$ $\Rightarrow 2 a-b=15$ Hence, the required value is 15...
Read More →Complete combustion of 3 g of ethane gives x .
Question: Complete combustion of $3 \mathrm{~g}$ of ethane gives $\mathrm{x} \times 10^{22}$ molecules of water. The value of $x$ is ______________ .(Round off to the Nearest Integer). $\left[\right.$ Use $: \mathrm{N}_{\mathrm{A}}=6.023 \times 10^{23} ;$ Atomic masses in $\mathrm{u}$$: C: 12.0 ; O: 16.0 ; H: 1.0]$ Solution: (18) No. of molecules $=0.3 \times 6.023 \times 10^{23}$ $=18.069 \times 10^{22}$...
Read More →Very-Short and Short-Answer Questions
Question: Very-Short and Short-Answer QuestionsIfk, (2k 1) and (2k+ 1) are the three successive terms of an AP, find the value ofk. Solution: It is given thatk, (2k 1) and (2k+ 1) are the three successive terms of an AP. $\therefore(2 k-1)-k=(2 k+1)-(2 k-1)$ $\Rightarrow k-1=2$ $\Rightarrow k=3$ Hence, the value ofkis 3....
Read More →Solve the following
Question: _______________grams of 3-Hydroxy propanal $(\mathrm{MW}=74)$ must be dehydrated to produce $7.8 \mathrm{~g}$ of acrolein $(\mathrm{MW}=56)\left(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\right)$ if the percentage yield is 64. (Round off to the Nearest Integer). [Given : Atomic masses: C: $12.0 \mathrm{u}, \mathrm{H}: 1.0 \mathrm{u}, \mathrm{O}: 16.0 \mathrm{u}$ ] Solution: (16)...
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