Respuesta :
Answer: 1.027 x 10^6 g= 1027kg
In this question, you are given the volume of the blimp (2.027×10^5 ft^3) and the density of the gas(0.179g/L). To answer this question, you need to convert the volume unit into liter. The calculation would be: 2.027×10^5 ft^3 x 28.3168L/ft3= 57.398 x 10^5L= 5.74x10^6L
Then to find the mass, multiply the volume with the density. The calculation would be: 5.74x10^6L x 0.179g/L= 1.027 x 10^6 g= 1027kg
In this question, you are given the volume of the blimp (2.027×10^5 ft^3) and the density of the gas(0.179g/L). To answer this question, you need to convert the volume unit into liter. The calculation would be: 2.027×10^5 ft^3 x 28.3168L/ft3= 57.398 x 10^5L= 5.74x10^6L
Then to find the mass, multiply the volume with the density. The calculation would be: 5.74x10^6L x 0.179g/L= 1.027 x 10^6 g= 1027kg
The mass of helium in the blimps is [tex]\boxed{10.2743{\text{ g}}}[/tex].
Further Explanation:
Density is defined as the mass of the substance per unit volume of the substance. It is represented by the symbol [tex]\rho[/tex]. The density of a substance is calculated as follows:
[tex]\rho = \dfrac{{\text{M}}}{{\text{V}}}[/tex]
Here,
[tex]\rho[/tex] is the density of the substance.
M is the mass of the substance.
V is the volume of the substance.
The formula to calculate the density of helium is as follows:
[tex]{\text{Density of helium}} = \dfrac{{{\text{Mass of helium}}}}{{{\text{Volume of helium}}}}[/tex] …… (1)
Rearrange equation (2) to calculate the mass of helium.
[tex]{\text{Mass of helium}} = \left( {{\text{Density of helium}}} \right)\left( {{\text{Volume of helium}}} \right)[/tex] …… (2)
The volume of the blimp is [tex]2.027 \times {10^5}{\text{ f}}{{\text{t}}^3}[/tex]. This is to be converted into L. The conversion factor for this is,
[tex]1{\text{ f}}{{\text{t}}^3} = 28.3168{\text{ L}}[/tex]
Since the blimp is filled with helium, the volume of the blimp becomes equal to that of helium. Therefore the volume of helium can be calculated as follows:
[tex]\begin{aligned}{\text{Volume of helium}} &= \left( {2.027 \times {{10}^5}{\text{ f}}{{\text{t}}^3}} \right)\left( {\frac{{28.3168{\text{ L}}}}{{1{\text{ f}}{{\text{t}}^3}}}} \right)\\&= 57.3982{\text{ L}}\\\end{aligned}[/tex]
Substitute 0.179 g/L for the density of helium and 57.3982 L for the volume of helium in equation (2).
[tex]\begin{aligned}{\text{Mass of helium}}&= \left( {{\text{0}}{\text{.179 g/L}}} \right)\left( {{\text{57}}{\text{.3982 L}}} \right)\\&= 10.2743{\text{ g}}\\\end{aligned}[/tex]
Therefore the mass of helium is 10.2743 g.
Learn more:
- Why is density an important property of matter? https://brainly.com/question/1593730
- Which element has the greatest density at STP? https://brainly.com/question/898857
Answer details:
Grade: Middle School
Chapter: Density
Subject: Chemistry
Keywords: density, mass, volume, helium, mass of helium, conversion factor, 10.2743 g, 0.179 g/L.
