Question

I have a problem, and I have the answer but I don't know where the solution comes from. ( I have to be able to solve these myself so please help me by answering the questions about the problem.)

If the reactants and products are confined to a volme of 10cm³ what is the pressure of the products (assume ideal gas behavior, complete decomposition of KClO₃, and neglect the volume of the solid product, KCl.

2KCLO₃(s) ---> 2KCL(s) + 3O₂(g)

Here is the answer given to me by the professor:

10gm KClO₃ (1mole/KCLO₃/122.55g KCLO₃) (3 mole O₂/2mole KCLO₃)=0.122 mole O₂

P=nRT/V=(0.122mole)(0.08206-atm/mol k)(1173k)/10cm³(1ml/1cm³)(1L/1000mL)

Answer = 1.2*10³ atm (1.173*10³ atm)

Questions about the problem: I understand the first half of the problem.

Where did the 0.08206l-atm come from?

Why was it divided by mol k (and how did he know to divide it by mol k)?

Where did the 1173k come from?

Where did the 1mL/1cm³ *1l/1000mL come from?

Please help!

Answer 1

(1): 0.08206-L.atm/mol k is the value of universal gas cnstant, R in terms of L and init atm.

R = 0.08206-Lxatm/mol k

(2): The unit of R can b derived from ideal gas equation, PV = nRT

=> R = PV / nT, where P is in 'atm', V is in 'L', n is in 'mole' and T is in K.

Hence unit of R becomes Lxatm / molxK.

Hence it is divided by mol.K

(3): It is given that KClO3 is completely decomposed and at 1173 K KClO3 is completely decomposed.

Hence temperature, T = 1173 K

(4): Here volume, V is given in cm³, however we need volume in terms of L. This is because we have taken the value of R in terms of L.atm / mol.k.

Hence inorder to cnvert cm3 to L, we need two conversion factors which are mL and L

Also 1 cm3 = 1 mL.

and 1000 mL = 1L

Hence we we multiplied the conversion factors 1mL/1cm3 and 1L/1000mL

L 0.01 L