A rigid nitrogen tank stored inside a laboratory has a pressure of $$30$$ atm at $$06:00$$ am when the temperature is $$27°$$C. At $$03:00$$ pm, when the temperature is $$45°$$C, the pressure in the tank will be ______ atm. [nearest integer]

We need to find the pressure of nitrogen gas at 45°C in a rigid tank, given the initial conditions.

Since the tank is rigid (constant volume) and the amount of gas is constant, we use Gay-Lussac's Law:

$$\frac{P_1}{T_1} = \frac{P_2}{T_2}$$

$$T_1 = 27°C + 273 = 300 \text{ K}$$

$$T_2 = 45°C + 273 = 318 \text{ K}$$

$$\frac{30}{300} = \frac{P_2}{318}$$

$$P_2 = \frac{30 \times 318}{300}$$

$$P_2 = \frac{9540}{300}$$

$$P_2 = 31.8 \text{ atm}$$

$$P_2 \approx 32 \text{ atm}$$

The pressure in the tank at 3:00 pm will be 32 atm.