A sample of ethane `(C_(2)H_(6))` gas has the same mass a `1.5 xx 10^(20)` moleucles of methane `(CH_(4))`. How many `C_(2)H_(6)` molecules does the sample of gas contain?

Explanation

To solve the problem, we need to find out how many molecules of ethane (C₂H₆) are present in a sample that has the same mass as 1.5 x 10²⁰ molecules of methane (CH₄).

### Step-by-Step Solution:

1. **Calculate the mass of the methane sample:**
- First, we need to find the mass of 1.5 x 10²⁰ molecules of methane.
- The molar mass of methane (CH₄) is 16 g/mol.
- Using Avogadro's number (6.022 x 10²³ molecules/mol), we can find the mass of the given number of molecules.
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