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A 4.05 g sample of an unknown gas at 69 C and 1.00 atm is stored in a 1.75 flask. What is the density of the gas?

Answer:

The Density of an Unknown Gas

The density of an unknown gas is determined by a number of factors, including its mass, volume, temperature, and pressure. In this case, we know that the mass of the gas sample is 4.05 g, the temperature of the gas is 69 degrees Celsius, and the pressure of the gas is 1.00 atm. The volume of the gas can be calculated by dividing the mass of the gas by its density.

Calculating the Volume of the Gas

To calculate the volume of the gas, we must first convert the given mass (4.05 g) and temperature (69 degrees Celsius) to SI units. The mass of the gas can be converted to kilograms using the conversion factor of 1 g = 0.001 kg. The temperature of the gas can be converted to Kelvin using the conversion factor of 1 degree Celsius = 274.15 K. Once the mass and temperature are in SI units, we can use the ideal gas law to calculate the volume of the gas:

The Ideal Gas Law

The ideal gas law states that the product of the pressure (P) of a gas multiplied by its volume (V) is equal to the product of its temperature (T) multiplied by its molar mass (M) and the ideal gas constant (R). The equation is written as: PV = RTM. In this case, the molar mass (M) and the ideal gas constant (R) can be assumed to be constant, so the equation can be rearranged to solve for the volume of the gas (V):

Calculating the Density of the Gas

Once the volume of the gas is known, the density can be calculated by dividing the mass of the gas (4.05 g) by its volume. The density of the gas is then equal to the mass of the gas divided by the volume of the gas, which is equal to the mass of the gas divided by the product of the pressure and the volume of the gas.

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