A 0.5 dm^3 flask contains gas A and 1 dm^3 flask contains gas B at the same temperature. If dens

step 1 The portion is a 0 .5 decimal Q plus contain gas A and 1 decimeter Q plus contain gas B. At the

A 0.5 dm^3 flask contains gas A and 1 dm^3 flask contains...

A $0.5 \mathrm{dm}^{3}$ flask contains gas $\mathrm{A}$ and $1 \mathrm{dm}^{3}$ flask contains gas $\mathrm{B}$ at the same temperature. If density of $\mathrm{A}$ is twice that of $\mathrm{B}$ and the molar mass of $\mathrm{A}$ is half of $\mathrm{B}$, then the ratio of pressure exerted by gases is (a) $P_{A} / P_{B}=2$ (b) $P_{A} / P_{B}=1$ (c) $P_{A} / P_{B}=4$ (d) $P_{\Lambda} / P_{B}=3$

A $0.5 \mathrm{dm}^{3}$ flask contains gas $\mathrm{A}$ and $1 \mathrm{dm}^{3}$ flask contains gas $\mathrm{B}$ at the same temperature. If density of $\mathrm{A}$ is twice that of $\mathrm{B}$ and the molar mass of $\mathrm{A}$ is half of $\mathrm{B}$, then the ratio of pressure exerted by gases is
(a) $P_{A} / P_{B}=2$
(b) $P_{A} / P_{B}=1$
(c) $P_{A} / P_{B}=4$
(d) $P_{\Lambda} / P_{B}=3$

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relation in thermodynamics that connects the pressure, volume, temperature, and number of moles of a gas. Under constant temperature conditions, this law shows that pressure is directly proportional to the number of moles and inversely proportional to the volume. This concept is crucial when comparing pressures of different gases in containers with varying volumes.

Density and Mass Relationship

Density, defined as mass per unit volume, plays a key role in determining the amount of gas present in a container. By relating density to the volume of a gas container, one can calculate the mass of the gas inside, which in turn is linked to the number of moles via the molar mass. This relationship is central to analyzing how different densities affect gas pressure.

Molar Mass

Molar mass is the mass of one mole of a substance and directly affects the conversion between the mass of a gas and the number of moles it contains. When combined with density and volume, molar mass enables the calculation of the number of moles of a gas, which is essential for applying the ideal gas law to determine pressure differences.

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