It takes 0.16 g of helium (He) to fill a balloon. How many grams of nitrogen (N2) would be required to fill the balloon to the same pressure, volume, and temperature?

We need to calculate the mass of nitrogen gas that can fill the balloon at same pressure, volume and temperature. This means that the moles of both the gases filling up balloon will be same.

So, to calculate the number of moles, we use the equation:

[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]

Given mass of Helium = 0.16 g

Molar mass of helium = 4.00 g/mol

Putting values in above equation, we get:

[tex]\text{Moles of helium}=\frac{0.16g}{4g/mol}=0.04mol[/tex]

Now, calculating the mass of nitrogen gas using same above equation, we get:

Moles of nitrogen gas = 0.04 moles

Molar mass of nitrogen gas = 28.01 g/mol

Putting values in above equation, we get:

[tex]0.04mol=\frac{\text{Mass of }N_2}{28.01g/mol}\\\\\text{Mass of }N_2=1.12g[/tex]

Hence, the mass of nitrogen gas required to fill the balloon is 1.12 grams.