an empty container has a mass of 658.57g. It has a mass of 659.45g after it has been filled with nitrogen gas at a pressure of 790 torr and a temperature of 15 deg C. When the container is evacuated and refilled with a certain element at a pressure of 745 torr and a temp of 26 deg C, it has a mass of 660.96g. What is the element?
Use PV = nRT to solve for V of the container with N2 gas.
Use PV = nRT with the unknown gas to determine n, then n = grams/molar mass to determine molar mass and from there the identity of the unknown gas.
To determine the element, we need to apply the ideal gas law equation, which states: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
First, let's find the initial number of moles of nitrogen gas in the container. We can rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
Given:
Pressure (P) = 790 torr
Temperature (T) = 15 °C (which needs to be converted to Kelvin) = 15 + 273.15 = 288.15 K
Mass of container filled with nitrogen gas = 659.45 g
Mass of empty container = 658.57 g
To find the volume (V) of the container, we can subtract the mass of the empty container from the mass of the container filled with nitrogen gas:
Mass of nitrogen gas = Mass of container filled with nitrogen gas - Mass of empty container
Mass of nitrogen gas = 659.45 g - 658.57 g = 0.88 g
Next, we need to convert the mass of nitrogen gas to moles using the molar mass of nitrogen (28.0134 g/mol):
Number of moles of nitrogen gas = Mass of nitrogen gas / Molar mass of nitrogen
Number of moles of nitrogen gas = 0.88 g / 28.0134 g/mol ≈ 0.0314 mol
Now that we have the number of moles of nitrogen gas, we can determine the volume (V) of the container using the ideal gas law equation:
V = (nRT) / P
V = (0.0314 mol * 0.0821 L·atm/mol·K * 288.15 K) / 790 torr
Converting torr to atm (1 atm = 760 torr):
V ≈ (0.0314 mol * 0.0821 L·atm/mol·K * 288.15 K) / (790 torr / 760 torr/atm)
V ≈ 0.898 L
Now, let's find the number of moles of the new element in the container. We can use the same equation, but with the new given values:
Pressure (P) = 745 torr
Temperature (T) = 26 °C (which needs to be converted to Kelvin) = 26 + 273.15 = 299.15 K
Mass of container filled with the new element = 660.96 g
First, calculate the mass of the new element:
Mass of the new element = Mass of container filled with the new element - Mass of empty container
Mass of the new element = 660.96 g - 658.57 g = 2.39 g
Now, find the number of moles of the new element:
Number of moles of the new element = Mass of the new element / Molar mass of the new element
Unfortunately, we don't have the molar mass or any other information about the new element in the given question. Without that information, we cannot determine the element using the given data.