Final answer:
After converting mass to moles and Celsius to Kelvin, the ideal gas law, PV = nRT, is applied to find the pressure, considering the volume, number of moles, ideal gas constant, and temperature.
Step-by-step explanation:
The subject of the question involves using the ideal gas law to calculate the pressure of nitrogen gas (N₂) stored in a cylinder. The ideal gas law is a fundamental equation in chemistry that relates pressure, volume, temperature, and moles of an ideal gas. To solve for the pressure, the equation can be written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in kelvins.
In this case, we first convert the mass of nitrogen gas to moles by using its molar mass (28.02 g/mol). Since we have 130.00 kg (or 130000 g) of N₂ and we need to find the total number of moles (n). n = 130000 g / 28.02 g/mol, which gives us the moles of nitrogen gas. Then we convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature (290 + 273.15 = 563.15 K). The volume of the gas is given as 1200.0 L.
Using these values and the constant R, we rearrange the ideal gas law to solve for P (pressure): P = (nRT)/V. Substituting in the values we've obtained, we can calculate the pressure of the nitrogen gas in the cylinder. In doing so, we provide a practical example of using chemistry to understand industrial processes such as the manufacture of ammonia.