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