Question

solve for the unknown variable:
p₁ = 1.5 atm
v₁ = 3.0 l
t₁ = 293 k
p₂ = 2.5 atm
v₂ =??
t₂ = 303 k
round to 3 sig figs. do not include units.
answer

Explanation:

Step1: Use the combined gas law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\).

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

\(V_2=\frac{P_1V_1T_2}{P_2T_1}\)

Step3: Substitute the given values

\(P_1 = 1.5\), \(V_1=3.0\), \(T_1 = 293\), \(P_2=2.5\), \(T_2 = 303\)
\(V_2=\frac{1.5\times3.0\times303}{2.5\times293}\)

Step4: Calculate the value

First, calculate the numerator: \(1.5\times3.0\times303 = 1363.5\)
Then, calculate the denominator: \(2.5\times293=732.5\)
\(V_2=\frac{1363.5}{732.5}\approx1.86\)

Answer:

\(1.86\)