The density of the sample of gas is \(\boxed{4\times10^{-3}\text{ g}/\text{cm}^3}\) or \(\boxed{0.004\text{ g}/\text{cm}^3}\).
Further Explanation:
Density of any kind of matter is defined as the total mass of that substance present in the volume occupied by it in the region of space.
Example (1) : If we consider equal amounts of tungsten and iron, then tungsten is heavier than iron because tungsten occupies lesser volume or lesser empty spaces inside it for a particular mass as compared to iron. Therefore, tungsten has density higher than that of iron.
Example (2): If we take 2 cubes of similar size (same volume) of tungsten and gold then the cube of gold will be heavier because its density is more than that of tungsten.
Given:
The mass of the sampleof the gas is \(30\text{ g}\).
The volume of the sample of the gas is \(7500\text{ cm}^3\).
Concept:
The density of the substance is defined as the ratio of the mass and volume.
\(\boxed{\rho=\dfrac{m}{V}}\) ......(1)
Here, \(\rho\) is the density of the sample ofthe gas, \(m\) is the mass of the sample of the gas and \(V\) is the volume occupied by the gas.
Substitute the value of \(m\) and \(V\) in equation (1).
\(\begin{aligned}\rho&=\dfrac{30\text{ g}}{7500\text{ cm}^3}\\&=4\times10^{-3}\text{ g}/\text{cm}^3\end{aligned}\)
Thus, the density of the sample of gas is \(\boxed{4\times10^{-3}\text{ g}/\text{cm}^3}\) or \(\boxed{0.004\text{ g}/\text{cm}^3}\).
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Answer Details:
Grade: middle school
Subject: Physics
Chapter: Matter
Keywords:
Density, sample of gas, 30g gas, volume, 7500 cm3, 7500 cm^3, mass, matter, volume occupied, sample, ratio,grams per centimeter cube
