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Step 1: List the given values.
To convert the temperature from degree Celsius to kelvin, add 273 to the temperature expressed in degree Celsius.
[tex]\begin{aligned} P_1 & = \text{0.329 atm} \\ T_1 & = 47^{\circ}\text{C} = \text{320 K} \\ T_2 & = 77^{\circ}\text{C} = \text{350 K} \end{aligned}[/tex]
Step 2: Calculate the final pressure by using Gay-Lussac's law.
[tex]\begin{aligned} \frac{P_1}{T_1} & = \frac{P_2}{T_2} \\ P_2T_1 & = P_1T_2 \\ \frac{P_2T_1}{T_1} & = \frac{P_1T_2}{T_1} \\ P_2 & = \frac{P_1T_2}{T_1} \\ & = \frac{(\text{0.329 atm})(\text{350 K})}{\text{320 K}} \\ & = \boxed{\text{0.360 atm}} \end{aligned}[/tex]
Hence, the new pressure will be 0.360 atm.
[tex]\\[/tex]
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