Hydrogen gas is spiked with tritium to the extent of 5.00 %...

Hydrogen gas is spiked with tritium to the extent of $5.00 \%$ by mass. What is the activity in curies of a $4.65 \mathrm{L}$ sample of this gas at $25.0^{\circ} \mathrm{C}$ and 1.05 atm pressure? [Hint: Use 3.02 u as the atomic mass of tritium and data from elsewhere in the text, as necessary.]

Key Concepts

Ideal Gas Law

This concept relates to the relationship between pressure, volume, temperature, and the number of moles of a gas, expressed as PV = nRT. It allows one to calculate the amount of gas (in moles) present in a given volume at specified conditions of temperature and pressure.

Radioactivity and Activity

Activity is a measure of the rate at which a radioactive substance decays, typically expressed in units such as curies or becquerels. It is determined by multiplying the decay constant by the number of radioactive atoms, providing a quantitative representation of how many decay events occur per unit time.

Percent Mass Composition

This concept involves determining the fraction by mass of a particular component within a mixture. By knowing the percentage of a specific isotope in a sample, one can calculate the mass and subsequently the number of moles or atoms of the isotope of interest.

Conversion Between Moles and Atoms

Using Avogadro's number, one can convert the amount of substance in moles to the actual number of atoms or molecules present. This conversion is crucial for linking the macroscopic measurements (like mass or moles) to microscopic counts necessary for calculating activity.

Decay Constant and Half-Life

The decay constant is a parameter that characterizes the probability of a single nucleus decaying per unit time, and it is related to the half-life of the radioactive substance. This relationship is essential in determining the rate of decay and, consequently, the activity of the substance.