# A spherical balloon can hold 1.2 liters of helium. The balloon has a mass of 26 milligrams when empty. Helium has a density of 0.1785 grams per liter. What is the mass of the balloon when it is filled with helium?

May 21, 2016

$\text{Mass of full balloon "=" Mass of empty balloon + mass of contents}$ $=$ ??g

#### Explanation:

So, we need first to calculate the mass of the helium in the balloon.

We are told that there are $1.2 \cdot L$ of $H e$, and also that the density ($\rho$) of $H e$ $=$ $0.1785 \cdot g \cdot {L}^{-} 1$.

But $\rho$ $=$ $\text{Mass"/"Volume}$. Thus $\text{Mass of gas"= " Volume} \times \rho$ $=$ $0.1785 \cdot g \cdot \cancel{{L}^{-} 1} \times 1.2 \cdot \cancel{L}$ $=$ $0.2142 \cdot g$. Note here that the units I used cancelled out to give an answer in grams as required.

Given this mass, the mass of the balloon is this mass + tare value $=$ $0.2142 \cdot g + 0.026 \cdot g$. Capisce? If I let it go, will it float or sink in the air; why?