Washington Policy Center's Todd Myers dissects Initiative 1631 - including how much it will raise prices at the pump. Initially, carbon taxes will add about $0.13 per gallon of gas in 2020, increasing to $0.73 per gallon in 2040, assuming a 3% inflation rate.
Keep in mind, these "gas taxes" are not protected by the 18th Amendment to the State Constitution and won't go to making your trip quicker, unlike the traditional gas tax. Read more:
https://www.washingtonpolicy.org/publications/detail/the-price-of-1631s-carbon-tax-at-the-pump