Which of the following gases will occupy the smallest volume at 300 K and 760 torr and why?

80 g diatomic oxygen
80 g methane
80 g hydrogen fluoride
All gases will occupy the same volume

Don't all ideal gases have the same volume at STP?

yes 1 atm right?

No, I think that's 22.4 L for a mole. To answer the question, I think I would use PV = nRT and calculate the volume of each. 80 grams of each is not the same number of moles.

i think its 1atm as well

ur all wrong

To determine which gas will occupy the smallest volume at a given temperature and pressure, we can utilize the ideal gas law equation:

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 in Kelvin.

By rearranging the equation, we have:

V = nRT / P

To compare the volumes of the three gases at the same temperature and pressure, we can consider the number of moles (n) of each gas. The number of moles of a gas can be calculated using the following equation:

n = mass / molar mass

where mass is the given amount of each gas, and molar mass is the mass of one mole of the gas.

Let's calculate the number of moles for each gas:

For diatomic oxygen (O2):
molar mass of O2 = 32 g/mol
n (O2) = 80 g / 32 g/mol = 2.5 mol

For methane (CH4):
molar mass of CH4 = 16 g/mol
n (CH4) = 80 g / 16 g/mol = 5 mol

For hydrogen fluoride (HF):
molar mass of HF = 20 g/mol
n (HF) = 80 g / 20 g/mol = 4 mol

Now, let's substitute these values into the volume equation:

V (O2) = (2.5 mol) * (0.0821 L·atm / (mol·K)) * (300 K) / (760 torr)
V (CH4) = (5 mol) * (0.0821 L·atm / (mol·K)) * (300 K) / (760 torr)
V (HF) = (4 mol) * (0.0821 L·atm / (mol·K)) * (300 K) / (760 torr)

Calculating the volumes:

V (O2) = 0.102 L
V (CH4) = 0.204 L
V (HF) = 0.163 L

From the calculations, we can see that oxygen (O2) will occupy the smallest volume, followed by hydrogen fluoride (HF), and methane (CH4) will occupy the largest volume.

Therefore, among the given gases, the diatomic oxygen (O2) will occupy the smallest volume at 300 K and 760 torr.