Question

Combined Gas Law Using the combined gas law above, identify the variables that would be in the numerator (A) and denominator (B) if you were to rearrange the gas law to solve for final pressure. Combined Gas Law Numerator (A): P1V1T2 P2V2T1 P1V1

Answer 1

Answer:

• Numerator (A):  P₁, V₁, and T₂.

• Denominator (B):  T₁ and V₂.

Explanation:

The combined gas law shows the pressure (P) and the Volume (V) are inversely related, and they both are directly proportional to the temperature (T).

This is the combined gas law:

$\frac{PV}{T}=constant\\ \\ \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

Where the superscripts 1 are used for one state and the superscripts 2 are used for another state.

If you use 1 for the initial state and 2 for the final state, then you want to solve for P₂.

So, using the general properties of equalities to isolate P₂, you have to multiply both sides by T₂ and divide both sides by V₂:

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\\ \\\frac{P_1V_1T_2}{T_1V_2}=P_2$

Then, you see that P₁, V₁, and T₂ are in the numerator, and T₁ and V₂ are in the denominator.

Answer 2

$P_{2$ = $\frac{A}{B}$

Numerator(A): $P_{1} V_{1} T_{2}$

Denominator(B): $T_{1}V_{2}$

$T_{2}$ = $\frac{A}{B}$

Numerator(A): $P_{2}V_{2}T_{1}$

Denominator(B): $P_{1}V_{1}$