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Solve the equation [tex]\frac{P_1 V_1}{n_1 T_1}=\frac{P_2 V_2}{n_2 T_3}[/tex] for [tex]n_1[/tex].
A. [tex]n_1=\frac{P_2 V_2 T_2 n_2}{P_1 V_1 T_1}[/tex] B. [tex]n_1=\frac{P_2 V_2 T_1}{P_1 V_1 n_2 T_3}[/tex] C. [tex]n_1=\frac{P_2 V_2 T_2}{P_1 V_1 T_1 n_2}[/tex] D. [tex]n_1=\frac{P_1 V_1 n_2 T_3}{P_2 V_2 T_1}[/tex]
To solve the given equation [tex]\(\frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_3}\)[/tex] for [tex]\(n_1\)[/tex], follow these steps:
1. Start with the given equation: [tex]\[
\frac{P_1 V_1}{n_1 T_1} = \frac{P_2 V_2}{n_2 T_3}
\][/tex]
2. To isolate [tex]\(n_1\)[/tex], first multiply both sides of the equation by [tex]\(n_1 T_1\)[/tex]: [tex]\[
P_1 V_1 = \frac{P_2 V_2 \cdot n_1 T_1}{n_2 T_3}
\][/tex]
3. Then, multiply both sides of the equation by [tex]\(\frac{n_2 T_3}{P_2 V_2}\)[/tex]: [tex]\[
n_1 T_1 = \frac{P_1 V_1 \cdot n_2 T_3}{P_2 V_2}
\][/tex]
4. Finally, divide both sides by [tex]\(T_1\)[/tex] to solve for [tex]\(n_1\)[/tex]: [tex]\[
n_1 = \frac{P_1 V_1 \cdot n_2 T_3}{P_2 V_2 \cdot T_1}
\][/tex]
Now we compare this derived expression with the provided options:
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