I got lost in the question please help!?

Question

Poloniu-210, a naturally occurring radioisotope, is an alpha emitter, with t1/2=136days. Assume that a sample of 210Po with a mass of 0.700mg was placed in a 250.0mL vessel, which was evacuated, sealed, and allowed to sit undisturbed. What would the pressure be inside the vessel (in mmHg) at 20 degrees celcius after 365 days if the alpha particles emitted had become Helium atoms?

Answer 1

There is definitely quite a lot to this question.  First off we need to determine how much helium is given off during the 1 year the 0.700 mg of Po-210 decays.  This means we need to determine how many half-lives ocurred over the 365 days, so just divide 365 by 136 to get 2.68 half-lives.  We can then use this to determine the mass of Po-210 left.

(initial amount)*(0.5)^(# of half-lives) = remaining amount

Or

(0.700 mg)*(0.5)^(2.68) = 0.109 mg  Po-210 remaining

Since Po-210 only decays by emitting alpha particles (aka: helium atoms), the difference between the initial and final masses of Po-210 will be the amount of He emitted:

0.700 mg - 0.109mg = 0.591mg He

Since helium is a gas and we want to know its pressure, we need to use the ideal gas equation: PV = nRT, or for our purposes: P= nRT/V.  Since we are given the volume and temperature, and of course R is a constant, the only thing we need to determine before solving for the pressure is n, the number of moles of helium gas in the chamber.  We just solved for the mass of He, so we just need its molecular weight to convert that mass into moles:

0.000591 g / (4.03 g/mol) = 0.000147 moles He

We put that into our rearranged ideal gas equation to give:

P = (0.000147moles)*[62.36367 (L*mmHg)/(mol*K)]*(293.15 K) / (0.2500 L)

= 10.7 mmHg