Question

Question #c7f43

Answer 1

Your gas contains `1.5 * 10^(23)` atoms.

Explanation:

The first important thing to notice is that the gas is tetra-atomic, `X_4`, which means that every molecule of gas contains 4 atoms.

So, if you know how many molecules you have, you can determine how many atoms are present by multiplying that number by 4.

In order to get the number of molecules, you need the number of moles of gas first. Notice that the temperature of the gas is `0^@"C"`, or 273.15 K, and that its pressure is 76 cmHg, which is equivalent to 1 atm.

`76cancel("cmHg") * (10cancel("mmHg"))/(1cancel("cmHg")) * "1 atm"/(760cancel("mmHg")) = "1 atm"`

These are actually the old conditions given for STP, which implies that 1 mole of your gas will occupy exactly 22.4 L - this is known as the molar volume of gas at STP.

SInce you're dealing with a volume of 1.4 L, the number of moles of gas present is

`1.4cancel("L") * "1 mole"/(22.4cancel("L")) = "0.0625 moles"`

To get the number of molecules present in this many moles, use the fact that 1 mole of a substance contains exactly `6.022 * 10^(23)` molecules of that substance - this is known as Avogadro's number.

`0.0625cancel("moles") * (6.022 * 10^(23)"molecules")/(1cancel("mole")) = 0.3764 * 10^(23)"molecules"`

Finally, get the number of atoms by multiplying this number by 4

`0.3764 * 10^(23)cancel("molecules") * "4 atoms"/(1cancel("molecule")) = 1.5056 * 10^(23)"atoms"`

I'll leave the answer rounded to two sig figs

`"no. atoms" = color(green)(1.5 * 10^(23))`