How does radioactive isotopes decay?

Answer:

                251.25 mL of O₂

Solution:

The balance chemical equation is as follow,

                             2 C₂H₂  +  5 O₂     →     4 CO₂  +  2 H₂O

As we know if the gas is acting ideally then 1 mole of any gas at standard temperature and pressure it will occupy exactly 22.4 L or  22400 mL of volume.

Keeping this in mind according to equation,

     44800 mL (2 mol) of C₂H₂ required  =  112000 mL (5 mol) of O₂

So,

                    100.50 mL of C₂H₂ will require  =  X mL of O₂

Solving for X,

                      X =  (100.5 mL × 112000 mL) ÷ 44800 mL

                      X  =  251.25 mL of O₂

The balanced reaction would be:

C2H2 + 5/2O2 = 2CO2 + H2O

We are given the amount of acetylene in the reaction. This will be the starting point of our calculation. We use the ideal gas equation to find for the number of moles.

n = PV / RT = 1.00(.1005 L) / (0.08206 atm L/mol K ) 273.15 K
n= 4.4837 x 10^-3 mol C2H2

4.4837 x 10^-3 mol C2H2 (5/2 mol O2/ 1 mol C2H2) = 0.0112 mol O2

V = nRT/P = 0.0112 mol O2 x 273.15 K x 0.08206 atm L/mol K / 1 atm
V=0.25125 L or 251.25 mL

Answer:

Mn: 3+

Cl: 7+

O: 2-

Explanation:

1) Compound given: Mn [ClO₄]₃

2) Initially you only know the oxidation state of O, since it is always 2-, except when it form peroxides, which is not the case.

3) So, you do not know the oxidation states neither of the Mn nor of the Cl, and you need some more information.

You might start from the ion [ClO₄] but you do not know its charge.

This ion comes from one of the oxoacids formed by Cl. Those are four different acids. These are them:

i) Oxidation state 1+: Cl₂O + H₂O → H₂Cl₂O₂ = HClO ⇒ ion ClO⁻

ii) Oxidation state 3+: Cl₂O₃ + H₂O → H₂Cl₂O₄ = HClO₂ ⇒ ion ClO₂⁻

iii) Oxidation state 5+: Cl₂O5 + H₂O → H₂Cl₂O₆ = HClO₃ ⇒ ion ClO₃⁻

iv) Oxidation state 7+: Cl₂O₇ + H₂O → H₂Cl₂O₈ = HClO₄ ⇒ ion ClO₄⁻

Finally, we have that our ion is ClO₄⁻ and the oxidation state of Cl is 7+.

4) Now you just have to find the oxidation state of Mn, for which you make a balance of charges:

Mn [ClO₄]₃

Since, the ion ClO₄⁻ has 1 negative charge, and there are 3 ions the total negative charge is 3-. Since the compound is neutral, you conclude that Mn has oxidation state 3+.

That according to this balance: 1(3+) + 3(1-) + 3 - 3 = 0.

5) Summarizing, the oxidation states are:

Mn: 3+

Cl: 7+

O: 2-