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# A given amount of gas occupies 10.0dm5 at 4atm and 273°C. The number of moles of...

### Question

A given amount of gas occupies 10.0dm5 at 4atm and 273°C. The number of moles of the gas present is [Molar volume of gas at s.t.p = 22.4dm$$^3$$]

### Options

A)
0.89 mol B)
1.90 mol
C)
3.80 mol
D)
5.70 mol

### Explanation:

To solve this question, we'll use the Ideal Gas Law, which is given by the formula:

$PV = nRT$

Where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin.

First, let's convert the given temperature from Celsius to Kelvin:

$T = 273 + 273 = 546\,\text{K}$

Next, we'll use the given values and the Ideal Gas Law to find the number of moles:

$4\,\text{atm} \times 10\,\text{dm}^3 = n \times 0.0821\,\frac{\text{atm}\cdot\text{dm}^3}{\text{mol}\cdot\text{K}} \times 546\,\text{K}$

Solve for n:

$n = \frac{4\,\text{atm} \times 10\,\text{dm}^3}{0.0821\,\frac{\text{atm}\cdot\text{dm}^3}{\text{mol}\cdot\text{K}} \times 546\,\text{K}} \approx 0.89\,\text{mol}$

Therefore, the number of moles of the gas present is approximately 0.89 mol, which corresponds to Option A.