Question

11 mark for review
pressure (p) 137.500 103.125 82.500 68.750 58.929 51.563 45.833 41.250
volume (v) 12 16 20 24 28 32 36 40
boyles law states that the pressure of a gas is inversely proportional to the volume of the gas at a constant temperature. the table gives the volume v, in milliliters (ml), of a gas for selected pressures p. which of the following gives a model for the volume of the gas as a function of pressure? (note: the units for pressure are not included.)
a v(p)=11.458p
b v(p)=1650p
c v(p)=\frac{11.458}{p}
d v(p)=\frac{1650}{p}

Explanation:

Step1: Recall Boyle's Law

Boyle's Law: $P_1V_1 = P_2V_2=k$ (constant).

Step2: Calculate the constant $k$

Take the first - row values: $P = 137.500$ and $V = 12$. Then $k=P\times V=137.500\times12 = 1650$.

Step3: Determine the function

Since $k = PV$, we can express $V$ as a function of $P$: $V(P)=\frac{k}{P}$. Substituting $k = 1650$, we get $V(P)=\frac{1650}{P}$.

Answer:

D. $V(P)=\frac{1650}{P}$