Question

1. gas mixing in a container

two containers are connected. container a has 2.0 mol of helium gas, volume 5.0 l at a pressure of 1atm. container b has 3.0 mol of neon gas, volume 10.0 l. both gases are at 300 k..
question:
calculate the volume of the helium gas if it now is at stp.

1. nuclear medicine

radioactive isotopes are used in medicine to diagnose and treat diseases. for example, technetium-99m is used in imaging, while iodine-131 treats thyroid conditions. these isotopes decay safely after use.
question:
why is it important that medical isotopes have short half-lives?

1. radiation types

Explanation:

Step1: Recall the ideal gas law at STP

At STP (Standard Temperature and Pressure), \(T = 273.15\space K\), \(P= 101.3\space kPa\) (or \(1\space atm\)). The ideal gas law is \(PV = nRT\), and for a fixed amount of gas (\(n\) is constant), we can use the combined gas law \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\). But since \(P_1 = P_2\) (both \(1\space atm\)), the formula simplifies to \(\frac{V_1}{T_1}=\frac{V_2}{T_2}\).

Step2: Substitute the known values

We know \(V_1 = 5.0\space L\), \(T_1=300\space K\), \(T_2 = 273.15\space K\).

$$V_2=\frac{V_1\times T_2}{T_1}$$

$$V_2=\frac{5.0\times273.15}{300}$$

$$V_2 = 4.5525\space L\approx4.6\space L$$

Answer:

\(4.6\space L\)