Question

a sample of $n_{2}(g)$ is in a container with a piston. the sample of $n_{2}(g)$ has a pressure of 1.21 atm, a temperature of $21^{circ}c$, and a volume of 1.03 l. if the pressure is increased to 4.47 atm at constant temperature, the new volume will be closest to which of the following?
a 0.190 l
b 0.279 l
c 3.59 l
d 5.25 l

Explanation:

Step1: Write down Boyle's Law formula

Boyle's Law states that \(P_1V_1 = P_2V_2\) (at constant temperature, where \(P\) is pressure and \(V\) is volume).

Step2: Rearrange the formula to solve for \(V_2\)

We can rewrite the formula as \(V_2=\frac{P_1V_1}{P_2}\).

Step3: Substitute the given values

Given \(P_1 = 1.21\space atm\), \(V_1=1.03\space L\), \(P_2 = 4.47\space atm\).
Substitute into the formula: \(V_2=\frac{1.21\times1.03}{4.47}\).
First, calculate \(1.21\times1.03 = 1.2463\).
Then, \(V_2=\frac{1.2463}{4.47}\approx0.279\space L\).

Answer:

B. \(0.279\space L\)