List of practice Questions

In the estimation of sulphur by Carius method, 0.468 g of an organic sulphur compound afforded 0.668 g of barium sulphate. Find out the percentage of sulphur in the given compound.
The reaction of cyanamide, \(NH_2CN(s)\), with dioxygen was carried out in a bomb calorimeter, and \(∆U\) was found to be \(–742.7\ kJ\ mol^{–1}\) at \(298\ K\). Calculate enthalpy change for the reaction at \(298\ K\).
\(NH_2CN(g)+\frac 32O_2(g)→N_2(g)+CO_2(g)+H_2O(l)\)
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kiloliters?
Find: (i) 64 \(\frac{1}{2}\) (ii) 32 \(\frac{1}{2}\) (iii) 125 \(\frac{1}{3}\)
If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.

Find: (i) 9 \(\frac{3}{2}\) (ii) 32 \(\frac{2}{5}\) (iii) 16 \(\frac{3}{4}\) (iv) 125 -\(\frac{1}{3}\)

In a process, 701 J of heat is absorbed by a system and 394 J of work is done by the system. What is the change in internal energy for the process?
A reaction, \(A+B→C+D+q\) is found to have a positive entropy change. The reaction will be

Rationalise the denominators of the following: 

(i) \(\frac{1 }{ \sqrt{7 }}\)

(ii) \(\frac{1 }{ \sqrt{7 }-\sqrt6}\)

(iii) \(\frac{1 }{ \sqrt{5}+\sqrt2}\)

(iv) \(\frac{1 }{ \sqrt{7}-2}\)

\(∆U^Θ\) of combustion of methane is – \(X\ kJ \ mol^{–1}\). The value of \(∆H^Θ\) is
The enthalpies of all elements in their standard states are:
The height of a cone is 15 cm. If its volume is 1570 cm3, find the diameter of its base. [Use \(\pi\) = 3.14]
For the process to occur under adiabatic conditions, the correct condition is:
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π =\(\frac{ c}{d}\). This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Assign oxidation numbers to the underlined elements in each of the following species: 
  1. \(NaH_2\underline PO_4\) 
  2. \(NaH\underline SO_4\) 
  3. \(H_4\underline P_2O_7\) 
  4. \(K_2\underline {Mn}O_4\) 
  5. \(Ca\underline O_2\) 
  6. \(Na\underline BH_4\) 
  7. \(H_2\underline S_2O_7\) 
  8. \(KAl(\underline SO_4)_2.12 H_2O\)
Choose the correct answer. A thermodynamic state function is a quantity

Classify the following numbers as rational or irrational:

(i) \(2 - \sqrt5\)  

(ii) \((3 + \sqrt23) - \sqrt23\) 

(iii) \(\frac{2 \sqrt{7}} { 7 \sqrt7}\)

(iv) \(\frac{1}{\sqrt{2}}\)

(v) 2π 

Classify the following numbers as rational or irrational : 

(i) \(\sqrt23 \)

(ii) \(\sqrt225 \)

(iii) 0.3796 

(iv) 7.478478... 

(v) 1.101001000100001...

Write three numbers whose decimal expansions are non-terminating non-recurring.

Look at several examples of rational numbers in the form \(\frac{p}{q}\) (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of \(\frac{1}{17}\)? Perform the division to check your answer
Express 0.99999 .... in the form \(\frac{p}{q}\) . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

You know that \(\frac{1}{7}\) = 0142857_ . . Can you predict what the decimal expansions of \(\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}\) are, without actually doing the long division? If so, how? [Hint : Study the remainders while finding the value of 1/7 carefully.]

0.3780 g of an organic chloro compound gave 0.5740 g of silver chloride in Carius estimation. Calculate the percentage of chlorine present in the compound.
Find the capacity in liters of a conical vessel with
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm