Question

a gas sample has a volume of 5.0 l and contains 1.5 moles of gas. if the amount of gas is increased to 3.0 moles while keeping temperature and pressure constant, what will be the new volume? the new volume is select one select one

Explanation:

Step1: Identify the gas law

This is a case of Avogadro's Law, which states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. The formula is $\frac{V_1}{n_1}=\frac{V_2}{n_2}$, where $V_1$ is the initial volume, $n_1$ is the initial number of moles, $V_2$ is the final volume, and $n_2$ is the final number of moles.

Step2: List the given values

We have $V_1 = 5.0\ L$, $n_1 = 1.5\ mol$, and $n_2 = 3.0\ mol$. We need to find $V_2$.

Step3: Rearrange the formula to solve for $V_2$

From $\frac{V_1}{n_1}=\frac{V_2}{n_2}$, we can rearrange it to $V_2=\frac{V_1\times n_2}{n_1}$.

Step4: Substitute the values into the formula

Substitute $V_1 = 5.0\ L$, $n_1 = 1.5\ mol$, and $n_2 = 3.0\ mol$ into the formula: $V_2=\frac{5.0\ L\times3.0\ mol}{1.5\ mol}$.

Step5: Calculate the value of $V_2$

First, calculate the numerator: $5.0\ L\times3.0\ mol = 15.0\ L\cdot mol$. Then divide by the denominator: $\frac{15.0\ L\cdot mol}{1.5\ mol}=10.0\ L$.

Answer:

The new volume is $10.0\ L$.