First, we need to convert the mass fraction of 15.0% by mass to grams of hydrogen peroxide in 100 g of solution:
{eq}\text{ grams of hydrogen peroxide} = (15.0%)times(100\text{ g solution}) = 15.0 \text{ g} {/eq}
Next, we need to calculate the molarity of the solution, which is defined as the number of moles of solute per liter of solution. To do this, we need to know the molar mass of hydrogen peroxide, which is 34.0147 g/mol.
Then, we can calculate the number of moles of hydrogen peroxide in 15.0 g:
{eq}\text{ moles of hydrogen peroxide} = \frac{15.0\text{ g}}{34.0147\text{ g/mol}} \approx 0.441 \text{ mol} {/eq}
Finally, we need to convert the volume of the solution from grams to milliliters using the density of hydrogen peroxide:
{eq}\text{ volume of solution} = \frac{100\text{ g solution}}{1.054\text{ g/mL}} \approx 94.7 \text{ mL} {/eq}
Now, we can calculate the molarity of the hydrogen peroxide solution:
{eq}\text{ molarity} = \frac{0.441\text{ mol}}{0.0947\text{ L}} \approx boxed{4.66 \text{ M}} {/eq}
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