[tex]V_{initial} = 752\:mL[/tex]
[tex]T_{initial} = 25.0^0C[/tex]
converting to Kelvin
TK = TC + 273
TK = 25.0 + 273 → TK = 298.0 → [tex]T_{initial} = 298.0\:K[/tex]
[tex]V_{final} = ? (in\:milliliters)[/tex]
[tex]T_{final} = 50.0^0C[/tex]
TK = TC + 273
TK = 50.0 + 273 → TK = 323.0 → [tex]T_{final} = 323.0\:K[/tex]
By the first Law of Charles and Gay-Lussac, we have:
[tex] \frac{ V_{i} }{ T_{i} } = \frac{ V_{f} }{ T_{f} }[/tex]
Solving:
[tex] \frac{ V_{i} }{ T_{i} } = \frac{ V_{f} }{ T_{f} }[/tex]
[tex]\frac{ 752 }{ 298.0 } = \frac{ V_{f} }{ 323.0 }[/tex]
Product of extremes equals product of means:
[tex]298.0* V_{f} = 752*323.0[/tex]
[tex]298.0 V_{f} = 242896[/tex]
[tex]V_{f} = \frac{242896}{298.0} [/tex]
[tex]\boxed{\boxed{V_{f} \approx 815.08\:mL}}\end{array}}\qquad\quad\checkmark[/tex]
