Question

question 6
5 points
assume we have a closed system where the ideal gas law applies. if we maintain a constant temperature and slowly decrease the pressure, the density must ______ in response.
a increase
b celebrate
c remain constant
d decrease

Explanation:

Step1: Recall ideal gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is temperature. Also, density $
ho=\frac{m}{V}$, and $n=\frac{m}{M}$ (where $m$ is mass and $M$ is molar mass). So, $P=\frac{
ho RT}{M}$ when we substitute $n=\frac{m}{M}$ and $
ho=\frac{m}{V}$ into $PV = nRT$.

Step2: Analyze the relationship

We are keeping $T$ constant. The equation $P=\frac{
ho RT}{M}$ can be written as $
ho=\frac{PM}{RT}$. Since $R$, $T$, and $M$ are constant, $
ho$ is directly proportional to $P$. When $P$ decreases, $
ho$ must also decrease.

Answer:

D. Decrease