A fixed mass of a gas occupies a volume of 150 cm 3 at a fixed temperature and a pressure of 1 atmosphere. What volume will the gas occupy at that temperature and at a pressure of 1.5 atmosphere?

Given, P 1 = 1 atm V 1 = 150 cm 3 P 2 = 1 . 5 atm V 2 = ? We know that PV = nRT The temperature is fixed, therefore, P 1 V 1 = P 2 V 2 V 2 = P 1 V 1 P 2 = 1 × 150 1 . 5 = 100 cm 3

State Avogadro's law. At a certain fixed temperature and pressure the molar volumes ( V / n ) of the real gases are nearly equal and at STP the limit is 22 . 4 Lmol - 1 . How Avogadro's law can be arrived at from this information obtained from experiments?

Avogadro’s law is a gas law which states that the total number of atoms/molecules of a gas (i.e. the amount of gaseous substance) is directly proportional to the volume occupied by the gas at constant temperature and pressure. At a certain fixed temperature and pressure the molar volumes ( V / n ) of the real gases are nearly equal and at STP the limit is 22 . 4 Lmol - 1 . Then, V 1 n 1 = V 2 n 2 V 1 n 1 = V 2 n 2 = K , where K is Avogadro constant. Which means that V α n As number of moles increases, volume increases.

A fixed mass of a gas occupies a volume of 520 cm 3 at - 13 ° C temperature. Keeping the pressure unchanged, when the gas is heated the volume of the gas increases to 700 cm 3 . What is the final temperature of the gas in degree celsius?

By ideal gas equation, PV = nRT As pressure is unchanged, we can write, V 1 T 1 = V 2 T 2 Given, V 1 = 520 cm 3 , V 2 = 700 cm 3 T 1 = ( 273 - 13 ) = 260 K 520 260 = 700 T 2 T 2 = 350 K The final temperature in degree Celsius ( 350 - 273 ) = 77 ° C

What is the product of pressure and volume of 2g of hydrogen at STP? H = 1

Given, Mass of hydrogen = 2 g Molecular weight of hydrogen = 2 The value of the universal gas constant R at STP = 8 . 314 Jmol − 1 K − 1 From ideal gas equation: PV = nRT = m M RT PV = 2 2 × 8 . 314 × 273 PV = 2 . 269 × 10 3 m 3 . mmHg

Under constant pressure, at what temperature in a degree Celsius, the volume of an ideal gas will be zero according to Charles law?

According to Charles law, the volume of the gas rises by 1 273 times its initial volume at 0 ° C with every degree increase in temperature at constant. V = V o + t 273 V o ; where V o is the initial volume and V is the final volume. If t = - 273 ; V = V o 1 - 273 273 ; then V ⇒ 0 Hence, at - 273 ° C , the volume of the gas becomes zero.

Establish the ideal gas equation on the basis of Boyle’s law, Charles law and Avogadro’s law.

Boyle's law, Charles' law and Avogadro's law can be combined in a single equation called ideal gas equation. This equation can be derived as given below: According to Boyle's law, V ∝ 1 P (at constant T and n )---------(i) According to Charles' law, V ∝ T (at constant P ) and ----------(ii) According to Avogadro's law, V ∝ n (at constant P and T )----------(iii), where n is the number of moles of the gas. On combining equations (i), (ii) and (iii) we get, V ∝ 1 P × T × n , V = R × nT P ----(iv), where, R is proportionality constant and is found to be independent of the nature of the gas and depends only on the amount of the gas taken. For one mole of any gas, the value of R is the same. Hence, R is called 'universal gas constant'. On rearranging the equation (iv), we get PV = nRT , this is called an ideal gas equation.