[tex]v_{\text{neon}} = \text{400 m/s}[/tex]
[tex]v_{\text{butane}}[/tex]
Step 1: Calculate the molecular weight of neon (Ne) and butane (C₄H₁₀).
For neon
[tex]MM_{\text{neon}} = \text{20.18 g/mol × 1}[/tex]
[tex]MM_{\text{neon}} = \text{20.18 g/mol}[/tex]
For butane
[tex]MM_{\text{neon}} = \text{(12.01 g/mol × 4) + (1.008 g/mol × 1)}[/tex]
[tex]MM_{\text{neon}} = \text{58.12 g/mol}[/tex]
Step 2: Calculate the velocity of butane.
[tex]\frac{v_{\text{butane}}}{v_{\text{neon}}} = \sqrt{\frac{MW_{\text{neon}}}{MW_{\text{butane}}}}[/tex]
[tex]v_{\text{butane}} = v_{\text{neon}}\sqrt{\frac{MW_{\text{neon}}}{MW_{\text{butane}}}}[/tex]
[tex]v_{\text{butane}} = (\text{400 m/s})(\sqrt{\frac{\text{20.18 g/mol}}{\text{58.12 g/mol}}})[/tex]
[tex]\boxed{v_{\text{butane}} = \text{235.7 m/s}}[/tex]
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